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Zorluk: OrtaSimple Interest

A small business owner takes out a loan of $15,000\$15,000 to repair commercial equipment. After exactly 8 months, the loan is paid off with a single payment of $15,900\$15,900. Assuming simple interest is applied, what is the annual interest rate on the loan?

  1. A
    6%6\%
  2. 9%9\%Cevap
  3. C
    4%4\%
  4. D
    7.5%7.5\%

Cevap

The annual simple interest rate on the loan is 9%9\%.
To find the annual interest rate, we first determine the total interest paid by subtracting the principal from the total payment ($15,900−$15,000=$900\$15,900 - \$15,000 = \$900). Next, we convert the 8-month term into years by dividing by 12, which gives 2/32/3 of a year. Plugging these into the simple interest formula, I=P×R×TI = P \times R \times T, gives 900=15,000×R×(2/3)900 = 15,000 \times R \times (2/3). Simplifying the right side yields 900=10,000×R900 = 10,000 \times R. Dividing both sides by 10,000 results in R=0.09R = 0.09, or 9%9\%.

Adım Adım Çözüm

1
Calculate the total amount of interest paid.
$15,900−$15,000=$900\$15,900 - \$15,000 = \$900
The simple interest formula requires the interest amount, which is the difference between the total payoff amount and the original principal.
2
Convert the loan duration from months into a fraction of a year.
8 months=812 year=23 year8 \text{ months} = \frac{8}{12} \text{ year} = \frac{2}{3} \text{ year}
Annual simple interest rates require the time variable (TT) to be expressed in years.
3
Substitute the known values into the simple interest formula (I=P×R×TI = P \times R \times T) and solve for the rate (RR).
$900=$15,000×R×23\$900 = \$15,000 \times R \times \frac{2}{3}
$900=$10,000×R\$900 = \$10,000 \times R
R=90010,000=0.09=9%R = \frac{900}{10,000} = 0.09 = 9\%
Isolating RR provides the annual interest rate in decimal form, which is then converted to a percentage.

Anahtar Kavram

Calculating the annual simple interest rate when given the principal, the total maturity amount, and a fractional time period in months.
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Konular

Simple Interest

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