Answer:
To calculate the monthly payment, total repayment, and total interest for Yolanda's loan of $27,000 at an interest rate of 7.65% for a term of 1 year, we can use the formula for monthly payments on an amortized loan:
The formula for the monthly payment $ M $ is given by:
$
M = P \frac{r(1 + r)^n}{(1 + r)^n - 1}
$
Where:
- $ P $ = principal amount (loan amount) = $27,000
- $ r $ = monthly interest rate = annual interest rate / 12 = 7.65% / 12 = 0.006375
- $ n $ = number of payments (months) = 1 year = 12 months
Substituting the values into the formula:
$
M = 27000 \frac{0.006375(1 + 0.006375)^{12}}{(1 + 0.006375)^{12} - 1}
$
Calculating $ (1 + r)^{12} $:
$
(1 + 0.006375)^{12} \approx 1.079304
$
Now substituting back into the payment formula:
$
M = 27000 \frac{0.006375 \times 1.079304}{1.079304 - 1}
$
Calculating the numerator and denominator:
$
M = 27000 \frac{0.006867}{0.079304} \approx 27000 \times 0.086609 \approx 2338.43
$
Thus, the monthly payment is approximately $2,338.43.
The total amount repaid over the term of the loan is calculated by multiplying the monthly payment by the number of payments:
$
\text{Total Repayment} = M \times n = 2338.43 \times 12 \approx 28,061.16
$
Thus, the total repayment amount is approximately $28,061.16.
The total interest paid over the life of the loan is the total repayment minus the principal:
$
\text{Total Interest} = \text{Total Repayment} - P = 28,061.16 - 27,000 \approx 1,061.16
$
Thus, the total interest paid is approximately $1,061.16.
In summary:
- Monthly Payment: $2,338.43
- Total Repayment: $28,061.16
- Total Interest: $1,061.16