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Difficulty: MediumSimple Interest Applications

A homeowner secures a personal bank loan of $4,500\$4,500 to renovate their kitchen. The loan agreement specifies an annual simple interest rate of 8%8\%. If the homeowner repays the entire loan in exactly 99 months, what is the total amount they must repay, including both principal and interest?

  1. A
    $4,527\$4,527
  2. $4,770\$4,770Answer
  3. C
    $4,860\$4,860
  4. D
    $7,740\$7,740

Answer

The total repayment amount is $4,770\$4,770.
The correct answer accurately calculates the interest for exactly 99 months ($270\$270) and adds it to the original principal ($4,500\$4,500) to yield the total repayment of $4,770\$4,770.

Step-by-Step Solution

1
Convert the annual interest rate from a percentage to a decimal.
8%=0.088\% = 0.08
Percentages must be expressed as decimals to be used in the simple interest formula.
2
Convert the loan term from months into years.
9 months=912 years=0.75 years9 \text{ months} = \frac{9}{12} \text{ years} = 0.75 \text{ years}
Since the interest rate is annual, the time variable in the formula must also be expressed in years.
3
Calculate the total simple interest using the formula I=PRTI = PRT.
I=$4,500×0.08×0.75=$270I = \$4,500 \times 0.08 \times 0.75 = \$270
This formula determines the total cost of borrowing the principal over the specified time period.
4
Calculate the total repayment amount by adding the principal and the interest.
A=$4,500+$270=$4,770A = \$4,500 + \$270 = \$4,770
The total repayment requires paying back the original loan amount plus the accrued interest.

Key Concept

Simple Interest Applications
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Topics

Simple Interest Applications

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