Read the financial scenario below and fill in the missing monetary amounts.

Cevap:A small business owner takes out a short-term loan to purchase new equipment. The loan accrues annual simple interest at a rate of

6\%

. After

9

months, the owner repays the loan in full with a single payment of

\$4,180

, which includes both the original principal and the accumulated interest.

The original principal amount of the loan was

\$【4000】

and the total interest charged was

\$【180】

The original principal amount was

4,000 and the interest charged was

180.

To find the original principal and interest from a total payoff amount, we must relate them using the formula

A = P(1 + RT)

. Because the rate is annual, the

9

months must be expressed as

0.75

years (or

3/4

). Substituting the knowns gives

4180 = P(1 + 0.06 \times 0.75)

, which simplifies to

4180 = 1.045P

. Dividing

4180

1.045

gives a principal of

\$4,000

. The interest is the total paid minus the principal:

4180 - 4000 = \$180

Convert the time period from months to years.

T = 9 \text{ months} = \frac{9}{12} \text{ years} = \frac{3}{4} \text{ year}

Annual simple interest rates require the time variable to be in years.

Set up the simple interest total amount formula.

A = P(1 + RT)

This formula relates the known total payoff amount (

A

) directly to the unknown principal (

P

Substitute the known values and simplify the interest multiplier.

4180 = P(1 + 0.06 \times \frac{3}{4}) \Rightarrow 4180 = P(1 + 0.045) = 1.045P

To create a single linear equation with

P

as the only unknown.

Solve for the principal (

P

P = \frac{4180}{1.045} = 4000

Dividing the total amount by the interest factor isolates the initial loan amount.

Calculate the total interest charged (

I

I = A - P = 4180 - 4000 = 180

The interest is the difference between the total amount paid and the original principal.

Calculating principal from a total maturity value (Principal + Interest) using fractional years in a simple interest context.

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