A business owner acquires a piece of industrial equipment under a hire purchase agreement.… — JAMB UTME

A business owner acquires a piece of industrial equipment under a hire purchase agreement. The cash price of the equipment is $₦2,500,000$ . The contract requires an initial deposit of $25\%$ of the cash price, with the remaining balance subject to simple interest of $12\%$ per annum calculated over a term of $2$ years. If the principal balance and total interest are repaid in equal monthly installments over the $2$ -year period, what is the amount of each monthly installment in Naira?

Answer: 96875 ₦

Answer

The amount of each monthly installment is ₦96,875.

To determine the monthly installment in a hire purchase transaction, deducting the

25\%

deposit (

₦625,000

) from the cash price (

₦2,500,000

) yields an unpaid balance of

₦1,875,000

. Applying

12\%

per annum interest for

2

years yields total interest of

₦450,000

. Combining the balance and total interest gives

₦2,325,000

. Dividing this total by

24

months yields

₦96,875

per month.

Step-by-Step Solution

Calculate the initial cash deposit required

0.25 \times ₦2,500,000 = ₦625,000

The buyer must pay 25% of the total cash price upfront.

Find the remaining unpaid principal balance

₦2,500,000 - ₦625,000 = ₦1,875,000

Interest is charged only on the balance remaining after paying the deposit.

Calculate the total simple interest accrued over 2 years

₦1,875,000 \times 0.12 \times 2 = ₦450,000

Simple interest formula is

I = P \times R \times T

where

P = ₦1,875,000

R = 12\%

, and

T = 2

years.

Calculate the total sum to be spread across monthly installments

₦1,875,000 + ₦450,000 = ₦2,325,000

The total installment debt consists of the outstanding principal balance plus the accrued interest.

Determine the value of each monthly installment

\frac{₦2,325,000}{24} = ₦96,875

A 2-year period comprises 24 equal monthly payments.

Key Concept

Calculation of Hire Purchase Interest and Monthly Installments

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