Financial Mathematics (Interest, Profit, Loss, and Depreciation) Practice Questions — JAMB UTME

Question 1Question →

A trader invested $\text{₦}50,000$ in a savings scheme that pays compound interest at a rate of $10\%$ per annum compounded annually. What is the total compound interest earned at the end of $2$ years?

\text{₦}10,500

\text{₦}60,500

\text{₦}10,000

\text{₦}5,000

Show answer & explanation

Answer: $\text{₦}10,500$

Answer

The total compound interest earned at the end of

2

years is

\text{₦}10,500

.

The compound interest is obtained by subtracting the principal from the total accumulated amount. Using

A = P(1 + r)^n

, the total amount is

\text{₦}60,500

. Subtracting the principal of

\text{₦}50,000

yields

\text{₦}10,500

.

Step-by-Step Solution

1

Calculate the total accumulated amount using the compound interest formula

A = P(1 + r)^n

A = 50,000 \times (1 + 0.10)^2 = 50,000 \times 1.21 = \text{₦}60,500

Determines the total value of the investment at the end of the duration.

2

Calculate the compound interest earned using

CI = A - P

CI = 60,500 - 50,000 = \text{₦}10,500

Subtracts the original principal from the total accumulated amount to find the interest portion.

Key Concept

Compound interest calculation

Question 2Question →

A company purchased a processing machine for $\text{₦}200,000$ . The value of the machine depreciates at a compound rate of $10\%$ per annum. At the end of $2$ years, the machine was sold at a profit of $15\%$ based on its depreciated value. What was the selling price of the machine?

\text{₦}184,000

\text{₦}186,300

\text{₦}192,000

\text{₦}207,000

Show answer & explanation

Answer: $\text{₦}186,300$

Answer

The selling price of the machine was

\text{₦}186,300

.

The depreciated value after 2 years at a compound rate of

10\%

per annum is calculated as

V = 200,000 \times (0.90)^2 = \text{₦}162,000

. Selling the machine at a

15\%

profit on this depreciated value gives a selling price of

162,000 \times 1.15 = \text{₦}186,300

.

Step-by-Step Solution

1

Calculate the depreciated value of the machine after 2 years using the compound depreciation formula

V = P(1 - r)^n

.

V = 200,000 \times (1 - 0.10)^2 = 200,000 \times (0.90)^2 = 200,000 \times 0.81 = \text{₦}162,000

.

Compound depreciation reduces the asset's remaining book value by

10\%

each year.

2

Calculate the

15\%

profit based on the depreciated value.

\text{Profit} = 15\% \text{ of } \text{₦}162,000 = 0.15 \times 162,000 = \text{₦}24,300$.

The problem specifies that profit is made on the depreciated value.

3

Calculate the selling price by adding the profit to the depreciated value.

\text{Selling Price} = \text{₦}162,000 + \text{₦}24,300 = \text{₦}186,300$.

Selling price is equal to book value plus profit earned.

Key Concept

Compound Depreciation and Percentage Profit on Book Value

Estimated Time:2m 0s

Question 3Question →

An entrepreneur bought a commercial printing machine for $\text{₦}300,000$ . If the machine depreciates in value at a compound rate of $15\%$ per annum, what is its value in Naira ( $\text{₦}$ ) at the end of $2$ years?

Show answer & explanation

Answer: 216750

Answer

The value of the machine at the end of 2 years is ₦216,750.

The value of the asset after 2 years is calculated using the reducing balance formula:

V_2 = V_0(1 - r)^2 = 300,000(0.85)^2 = \text{₦}216,750

.

Step-by-Step Solution

1

Identify given parameters

Initial principal value

V_0 = 300,000

, annual depreciation rate

r = 0.15

, duration

n = 2

years.

Establishing known variables simplifies formula substitution.

2

Apply compound depreciation formula

V_2 = V_0(1 - r)^2 = 300,000(1 - 0.15)^2

Asset values decrease multiplicatively per period under compound depreciation.

3

Compute the final depreciated value

V_2 = 300,000 \times (0.85)^2 = 300,000 \times 0.7225 = 216,750

Multiplying the initial amount by the combined depreciation factor yields the residual asset value.

Key Concept

Compound Depreciation

Question 4Question →

A cooperative society invested $\text{₦}80,000$ in a fixed deposit fund that pays compound interest at a rate of $10\%$ per annum compounded annually. What is the total compound interest earned by the cooperative society at the end of $2$ years?

\text{₦}16,000

\text{₦}16,800

\text{₦}96,000

\text{₦}96,800

Show answer & explanation

Answer: $\text{₦}16,800$

Answer

\text{₦}16,800

Using the compound interest formula for total amount,

A = P\left(1 + \frac{r}{100}\right)^n

, with principal

P = \text{₦}80,000

, rate

r = 10\%

, and time

n = 2

years:

A = 80000 \times (1.1)^2 = \text{₦}96,800

. The interest earned is the difference between the total amount and the principal:

I = 96800 - 80000 = \text{₦}16,800

.

Step-by-Step Solution

1

Calculate the total accumulated amount

A

using the compound interest formula

A = P\left(1 + \frac{r}{100}\right)^n

A = 80000 \times \left(1 + \frac{10}{100}\right)^2 = 80000 \times (1.1)^2 = 80000 \times 1.21 = \text{₦}96,800

The formula yields the full final balance after compound growth over 2 years.

2

Subtract the initial principal

P

from the total amount

A

to find the compound interest earned

I

I = A - P = 96800 - 80000 = \text{₦}16,800

Interest earned represents only the financial growth beyond the starting capital.

Key Concept

Compound Interest and Total Accumulated Amount

Question 5Question →

A merchant bought a power generator for $\text{₦}120,000$ and sold it to a retailer at a profit of $20\%$ . The retailer later sold the generator to a customer at a loss of $15\%$ . How much did the customer pay for the generator?

\text{₦}122,400

\text{₦}126,000

\text{₦}110,400

\text{₦}144,000

Show answer & explanation

Answer: $\text{₦}122,400$

Answer

The customer paid

\text{₦}122,400

for the generator.

The merchant sells the generator for

120\%

of

\text{₦}120,000

, which equals

\text{₦}144,000

. The retailer then sells it at

85\%

of

\text{₦}144,000

, yielding

\text{₦}122,400

.

Step-by-Step Solution

1

Calculate the selling price of the generator from the merchant to the retailer.

\text{Selling Price}_1 = \text{₦}120,000 \times \left(1 + \frac{20}{100}\right) = \text{₦}120,000 \times 1.20 = \text{₦}144,000

The merchant makes a

20\%

profit on the initial cost price of

\text{₦}120,000

.

2

Calculate the selling price from the retailer to the final customer.

\text{Selling Price}_2 = \text{₦}144,000 \times \left(1 - \frac{15}{100}\right) = \text{₦}144,000 \times 0.85 = \text{₦}122,400

The retailer incurs a

15\%

loss calculated relative to their purchase price of

\text{₦}144,000

.

Key Concept

Successive Percentage Profit and Loss

Question 6Question →

An artisan deposited $\text{₦}20,000$ into a savings account that pays a compound interest rate of $10\%$ per annum compounded annually. What is the total compound interest earned at the end of $2$ years?

\text{₦}4,200

\text{₦}24,200

\text{₦}4,000

\text{₦}2,000

Show answer & explanation

Answer: $\text{₦}4,200$

Answer

The total compound interest earned after 2 years is

\text{₦}4,200

.

The correct answer is obtained by calculating the total amount after 2 years at

10\%

compound interest, which is

20,000 \times (1.10)^2 = \text{₦}24,200

, and then subtracting the principal of

\text{₦}20,000

to get

\text{₦}4,200

.

Step-by-Step Solution

1

Calculate the total accumulated amount (

A

) after 2 years using the compound interest formula

A = P\left(1 + \frac{R}{100}\right)^n

.

A = 20,000 \left(1 + \frac{10}{100}\right)^2 = 20,000 \times (1.1)^2 = 20,000 \times 1.21 = \text{₦}24,200

.

Determines the total value of the investment at the end of the 2-year period.

2

Subtract the principal (

P

) from the total accumulated amount (

A

) to find the interest earned (

I = A - P

).

I = 24,200 - 20,000 = \text{₦}4,200

.

Isolates the interest earned from the initial principal amount.

Key Concept

Compound Interest Calculation

Estimated Time:45s

Question 7Question →

A business owner borrowed $\text{₦}150,000$ to expand his store at a compound interest rate of $8\%$ per annum, compounded annually. What is the total compound interest he will pay at the end of 2 years?

\text{₦}24,960

\text{₦}174,960

\text{₦}24,000

\text{₦}26,960

Show answer & explanation

Answer: $\text{₦}24,960$

Answer

The total compound interest paid at the end of 2 years is

\text{₦}24,960

.

The total compound interest is obtained by calculating the interest accrued in each period (

12,000

in Year 1 and

12,960

in Year 2) and summing them to get

\text{₦}24,960

. Alternatively, using the compound interest formula

I = P(1 + r)^n - P

,

I = 150,000(1.08)^2 - 150,000 = 174,960 - 150,000 = \text{₦}24,960

.

Step-by-Step Solution

1

Calculate the interest for the first year.

\text{Interest}_1 = \frac{8}{100} \times 150,000 = \text{₦}12,000

Interest in the first year is calculated on the initial principal.

2

Find the principal for the second year.

\text{Principal}_2 = 150,000 + 12,000 = \text{₦}162,000

Under compound interest, the first year's interest is added to the initial principal.

3

Calculate the interest for the second year.

\text{Interest}_2 = \frac{8}{100} \times 162,000 = \text{₦}12,960

Interest in the second year is calculated on the updated principal.

4

Sum the interest from both years to find the total compound interest.

\text{Total Interest} = 12,000 + 12,960 = \text{₦}24,960

The total compound interest is the sum of interest accumulated in each compounding period.

Key Concept

Compound Interest

Estimated Time:1m 30s

Question 8Question →

A trader bought a set of solar panels for $\text{₦}160,000$ . He marked up the cost price by $25\%$ to fix the marked price. During a trade fair, he offered a $10\%$ discount on the marked price. What is his net profit in Naira?

Show answer & explanation

Answer: 20000

Answer

The net profit made by the trader is ��20,000.

First, find the marked price by adding a 25% markup to the cost price: ₦160,000 × 1.25 = ₦200,000. Next, calculate the selling price after a 10% discount on the marked price: ₦200,000 × 0.90 = ₦180,000. Finally, subtract the cost price from the selling price to find the net profit: ₦180,000 - ₦160,000 = ₦20,000.

Step-by-Step Solution

1

Calculate the marked price

Marked Price = ₦200,000

The marked price is 125% of the original cost price of ₦160,000.

2

Calculate the selling price after discount

Selling Price = ₦180,000

A 10% discount reduces the marked price by ₦20,000.

3

Determine the net profit

Net Profit = ₦20,000

Net profit is the difference between the selling price (₦180,000) and the cost price (₦160,000).

Key Concept

Markup, Discount, and Profit Calculations

Question 9Question →

A trader bought a quantity of palm oil. He sold $\frac{1}{3}$ of the total quantity at a profit of $20\%$ , $\frac{1}{2}$ of the remaining palm oil at a loss of $10\%$ , and the rest of the palm oil at a profit of $x\%$ . If his overall profit on the entire transaction was $15\%$ , what is the value of $x$ ?

Show answer & explanation

Answer: 35

Answer

The value of

x

is

35

.

The palm oil is divided into three equal portions of

\frac{1}{3}

each. The first portion contributes

\frac{20}{3}\%

profit, the second portion contributes a loss of

-\frac{10}{3}\%

, and the final portion contributes

\frac{x}{3}\%

profit. Summing these contributions yields

\frac{10 + x}{3}\%

. Equating this to the target overall profit of

15\%

gives

10 + x = 45

, which solves to

x = 35

.

Step-by-Step Solution

1

Determine the fractional portion of palm oil sold at each stage.

First portion =

\frac{1}{3}

. Remaining after first sale =

1 - \frac{1}{3} = \frac{2}{3}

. Second portion =

\frac{1}{2} \times \frac{2}{3} = \frac{1}{3}

. Final portion =

1 - \left(\frac{1}{3} + \frac{1}{3}\right) = \frac{1}{3}

.

Finding the exact fraction of the total quantity sold at each step is necessary to weight their respective profit/loss rates correctly.

2

Formulate the net percentage profit equation.

\text{Net Profit } \% = \left(\frac{1}{3} \times 20\%\right) + \left(\frac{1}{3} \times (-10\%)\right) + \left(\frac{1}{3} \times x\%\right) = \frac{20 - 10 + x}{3}\% = \frac{10 + x}{3}\%

The overall profit percentage is the sum of individual fractional contributions, treating loss as a negative percentage.

3

Set the net profit equal to

15\%

and solve for

x

.

\frac{10 + x}{3} = 15 \implies 10 + x = 45 \implies x = 35

Solving this linear equation gives the required profit percentage for the final portion.

Key Concept

Weighted Average Profit and Loss across fractional components of an asset

Estimated Time:2m 0s

Question 10Question →

A businesswoman invested $\text{₦}50,000$ in a financial fund. Part of the money was invested at a simple interest rate of $6\%$ per annum, and the remaining part was invested at $8\%$ simple interest per annum. If the total interest earned at the end of $1$ year was $\text{₦}3,600$ , what was the amount, in Naira, invested at the $8\%$ interest rate?

Show answer & explanation

Answer: 30000

Answer

The amount invested at the

8\%

interest rate is

\text{₦}30,000

.

Setting up the linear equation for annual simple interest gives

0.06(50,000 - x) + 0.08x = 3,600

. Simplifying this yields

3,000 + 0.02x = 3,600

, which solves to

x = 30,000

. Thus,

\text{₦}30,000

was invested at

8\%

.

Step-by-Step Solution

1

Define variables for the two investment amounts.

Let

x

be the amount in Naira invested at

8\%

, so

(50,000 - x)

is the amount invested at

6\%

.

The total capital of

\text{₦}50,000

is split into two distinct portions.

2

Formulate the total interest expression using the simple interest formula

I = \frac{P \times R \times T}{100}

.

\frac{6}{100}(50,000 - x) + \frac{8}{100}x = 3,600

The sum of annual interests from both parts equals the total interest earned of

\text{₦}3,600

.

3

Expand the terms and solve the linear equation for

x

.

3,000 + 0.02x = 3,600 \implies 0.02x = 600 \implies x = 30,000

Isolating

x

yields the exact principal amount allocated to the

8\%

interest rate.

Key Concept

Simple Interest and Allocation of Principal across Different Interest Rates

Estimated Time:1m 30s

Question 11Question →

A farmer bought a motorcycle for $\text{₦}250,000$ and later sold it at a profit of $12\%$ . What is the selling price of the motorcycle in Naira?

Show answer & explanation

Answer: 280000

Answer

The selling price of the motorcycle is ₦280,000.

The cost price of the motorcycle is

\text{₦}250,000

. A profit of

12\%

means an additional

\frac{12}{100} \times 250,000 = \text{₦}30,000

. Adding this profit to the cost price gives a selling price of

\text{₦}250,000 + \text{₦}30,000 = \text{₦}280,000

.

Step-by-Step Solution

1

Calculate the profit amount in Naira

Profit = ₦30,000

Profit is calculated as 12% of the original cost price of ₦250,000.

2

Determine the final selling price

Selling Price = ₦280,000

Selling price equals cost price plus the profit made.

Key Concept

Percentage Profit and Selling Price

Question 12Question →

A logistics firm purchased a commercial delivery van for $\text{₦}800,000$ . If the value of the van depreciates by $10\%$ in the first year and by $15\%$ in the second year, what is the value of the van at the end of the second year?

\text{₦}612,000

\text{₦}600,000

\text{₦}188,000

\text{₦}648,000

Show answer & explanation

Answer: $\text{₦}612,000$

Answer

\text{₦}612,000

To find the remaining value of an asset undergoing successive annual depreciation, multiply the initial cost by each annual retention factor

(1 - r)

. For Year 1 at

10\%

, the value retention factor is

0.90

, making the value

\text{₦}720,000

. For Year 2 at

15\%

, the retention factor is

0.85

, yielding a final value of

\text{₦}720,000 \times 0.85 = \text{₦}612,000

.

Step-by-Step Solution

1

Calculate the value of the van at the end of the first year after a 10% depreciation.

\text{Value after Year 1} = \text{₦}800,000 \times \left(1 - \frac{10}{100}\right) = \text{₦}800,000 \times 0.90 = \text{₦}720,000

Depreciation decreases the principal asset value by the specified percentage.

2

Calculate the value of the van at the end of the second year after a 15% depreciation on the year-one value.

\text{Value after Year 2} = \text{₦}720,000 \times \left(1 - \frac{15}{100}\right) = \text{₦}720,000 \times 0.85 = \text{₦}612,000

Successive depreciation is compounded on the reduced value at the start of each period.

Key Concept

Successive Asset Depreciation

Question 13Question →

A trader deposited $\text{₦}40,000$ in a microfinance bank offering compound interest at the rate of $10\%$ per annum, compounded annually. What is the total interest earned by the trader at the end of $2$ years?

\text{₦}8,000

\text{₦}8,400

\text{₦}40,400

\text{₦}48,400

Show answer & explanation

Answer: $\text{₦}8,400$

Answer

The total interest earned by the trader at the end of

2

years is

\text{₦}8,400

.

Using the compound interest formula

A = P(1 + r)^n

, the total accumulated amount after 2 years is

40,000 \times (1.1)^2 = \text{₦}48,400

. Subtracting the original principal of

\text{₦}40,000

gives the compound interest earned:

48,400 - 40,000 = \text{₦}8,400

.

Step-by-Step Solution

1

Calculate the total accumulated amount (

A

) using the compound interest formula

A = P\left(1 + \frac{R}{100}\right)^n

.

A = 40,000\left(1 + \frac{10}{100}\right)^2 = 40,000 \times (1.1)^2 = 40,000 \times 1.21 = \text{₦}48,400

.

The compound interest formula yields the total value of the investment after 2 years.

2

Subtract the initial principal (

P

) from the total accumulated amount (

A

) to find the compound interest (

I

).

I = A - P = 48,400 - 40,000 = \text{₦}8,400

.

Interest earned is the difference between total final amount and initial principal.

Key Concept

Calculation of compound interest vs total accumulated amount

Question 14Question →

An investor deposited $\text{₦}60,000$ into a financial scheme for $2$ years at an annual interest rate of $r\%$ . If the difference between the compound interest (compounded annually) and the simple interest earned over the $2$ -year period is $\text{₦}384$ , calculate the value of $r$ .

Show answer & explanation

Answer: 8

Answer

The interest rate r is 8%

For a two-year investment period, the difference between compound interest (compounded annually) and simple interest equals the interest earned in the second year on the first year's interest, which is

P \left(\frac{r}{100}\right)^2

. Setting

60,000 \times \frac{r^2}{10,000} = 384

yields

6r^2 = 384

, giving

r^2 = 64

and

r = 8\%

.

Step-by-Step Solution

1

Express the simple interest for 2 years in terms of r

I_{\text{SI}} = 1,200r

Simple interest is calculated directly on the principal amount for the full term.

2

Express the compound interest for 2 years in terms of r

I_{\text{CI}} = 1,200r + 6r^2

Compound interest includes interest earned on the first year's interest.

3

Set up the equation for the difference between compound and simple interest

(1,200r + 6r^2) - 1,200r = 384 \implies 6r^2 = 384

The difference between CI and SI over 2 years isolates the interest-on-interest component.

4

Solve for r

r = 8

Dividing 384 by 6 gives 64, and taking the principal square root yields 8.

Key Concept

Difference between Compound Interest and Simple Interest for 2 years

Question 15Question →

A poultry farmer in Ogun State took a loan of $\text{₦}120,000$ from a cooperative society at an annual interest rate of $5\%$ , compounded annually. What is the total interest paid by the farmer at the end of $2$ years?

\text{₦}12,300

\text{₦}132,300

\text{₦}12,000

\text{₦}132,000

Show answer & explanation

Answer: $\text{₦}12,300$

Answer

The total compound interest paid at the end of 2 years is

\text{₦}12,300

.

The total compound interest is determined by calculating the accumulated amount

A = 120,000 \times (1.05)^2 = \text{₦}132,300

and subtracting the original principal of

\text{₦}120,000

, yielding

\text{₦}12,300

.

Step-by-Step Solution

1

Identify the given values for principal, rate, and time

Principal

P = \text{₦}120,000

, Rate

r = 5\% = 0.05

, Time

t = 2\text{ years}

These parameters are required to substitute into the compound amount formula.

2

Calculate the total accumulated amount

A

after 2 years

A = P(1 + r)^t = 120,000 \times (1 + 0.05)^2 = 120,000 \times 1.1025 = \text{₦}132,300

The compound interest formula yields the total balance including the initial principal.

3

Subtract the initial principal from the total accumulated amount to determine interest

Compound Interest

= A - P = 132,300 - 120,000 = \text{₦}12,300

Interest is the extra amount generated beyond the original loan amount.

Key Concept

Compound Interest vs Total Accumulated Amount

Estimated Time:1m 30s

Question 16Question →

A boutique owner in Enugu borrowed $\text{₦}80,000$ to expand her business at an annual interest rate of $15\%$ , compounded annually. If she repays the loan in full after $2$ years, what is the total interest she paid on the loan?

\text{₦}24,000

\text{₦}25,800

\text{₦}27,600

\text{₦}105,800

Show answer & explanation

Answer: $\text{₦}25,800$

Answer

The total interest paid on the loan after 2 years is

\text{₦}25,800

.

The compound interest is calculated year by year. In the first year, the interest paid is

15\%

of

\text{₦}80,000 = \text{₦}12,000

, raising the balance to

\text{₦}92,000

. In the second year, the interest paid is

15\%

of

\text{₦}92,000 = \text{₦}13,800

. Adding the two yearly interest payments gives

\text{₦}12,000 + \text{₦}13,800 = \text{₦}25,800

.

Step-by-Step Solution

1

Calculate the interest for the first year.

Interest for Year 1 =

15\%

of

\text{₦}80,000 = \frac{15}{100} \times 80,000 = \text{₦}12,000

.

In compound interest, interest for the first period is calculated on the initial principal.

2

Determine the amount at the end of the first year, which becomes the principal for the second year.

Principal for Year 2 =

\text{₦}80,000 + \text{₦}12,000 = \text{₦}92,000

.

Compound interest adds earned interest to the principal for subsequent period calculations.

3

Calculate the interest for the second year.

Interest for Year 2 =

15\%

of

\text{₦}92,000 = \frac{15}{100} \times 92,000 = \text{₦}13,800

.

Interest in year 2 is computed on the updated principal balance of

\text{₦}92,000

.

4

Sum the interest amounts from both years to find total interest paid.

Total Interest =

\text{₦}12,000 + \text{₦}13,800 = \text{₦}25,800

.

The total interest is the sum of interest accumulated across each compounding period.

Key Concept

Compound Interest Calculation

Estimated Time:1m 30s

Question 17Question →

A cooperative society in Akure granted a loan of $\text{₦}160,000$ to a farmer at an interest rate of $12\%$ per annum, compounded annually. What is the total compound interest owed at the end of $2$ years?

\text{₦}40,704

\text{₦}200,704

\text{₦}38,400

\text{₦}19,200

Show answer & explanation

Answer: $\text{₦}40,704$

Answer

The total compound interest owed at the end of 2 years is

\text{₦}40,704

.

The compound interest is obtained by calculating the accumulated amount

A = 160,000 \times (1.12)^2 = \text{₦}200,704

and then subtracting the principal of

\text{₦}160,000

to get

\text{₦}40,704

.

Step-by-Step Solution

1

Identify the given financial variables

Principal

P = \text{₦}160,000

, Rate

R = 12\%

, Time

n = 2

years.

Establishing the parameters needed for the compound interest formula.

2

Calculate the total accumulated amount

A

using the formula

A = P\left(1 + \frac{R}{100}\right)^n

A = 160,000 \times \left(1 + 0.12\right)^2 = 160,000 \times (1.12)^2 = 160,000 \times 1.2544 = \text{₦}200,704

.

Determines the total value of the loan including principal and accrued compound interest after 2 years.

3

Subtract the principal

P

from the total amount

A

to find the compound interest

CI

CI = A - P = 200,704 - 160,000 = \text{₦}40,704

.

Isolates the interest portion from the total accumulated balance.

Key Concept

Compound Interest Calculation

Financial Mathematics (Interest, Profit, Loss, and Depreciation)

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Common Mistakes

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Common Mistakes

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Common Mistakes

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Common Mistakes

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Common Mistakes

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Common Mistakes

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Common Mistakes

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Common Mistakes

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Common Mistakes

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Common Mistakes

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Common Mistakes

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Common Mistakes