To calculate the amount of interest earned on an investment with compounded interest, we can use the formula:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) = the future value of the investment/loan, including interest
- \( P \) = the principal investment amount (initial deposit or loan amount)
- \( r \) = the annual interest rate (decimal)
- \( n \) = the number of times that interest is compounded per unit \( t \)
- \( t \) = the time the money is invested or borrowed for, in years
Given:
- \( P = 9,875 \)
- \( r = 4.8% = 0.048 \)
- \( n = 12 \) (monthly compounding)
- \( t = 12 \)
Now we plug in the values:
\[ A = 9,875 \left(1 + \frac{0.048}{12}\right)^{12 \times 12} \]
Calculating inside the parentheses:
\[ 1 + \frac{0.048}{12} = 1 + 0.004 = 1.004 \]
Now calculate the exponent:
\[ 12 \times 12 = 144 \]
So we raise \( 1.004 \) to the power of 144:
\[ A = 9,875 \times (1.004)^{144} \]
Calculating \( (1.004)^{144} \):
Using a calculator:
\[ (1.004)^{144} \approx 1.7469 \]
Now, multiply by the principal:
\[ A \approx 9,875 \times 1.7469 \approx 17,266.34 \]
Now, to find the interest earned:
\[ \text{Interest} = A - P = 17,266.34 - 9,875 \approx 7,391.34 \]
Since this differs from the options given, let’s double-check both our calculations, rounding, and look closely:
- \( A \approx 17,266.34 \)
- Interest earn = \( 17,266.34 - 9,875 = 7,391.34 \)
None of the provided options are exact matches, but the closest option to this calculated interest is $7,457.95. Therefore, the approximate answer for the interest earned on the investment is:
$7,457.95
1 answer