Question

Calculate the total payback for a $3,500 loan at 8% annual interest with monthly payments for two years.
My answer is 3,815.28 is that correct?

Answer 1

To find the total payback of a $3,500 loan at 8% annual interest with monthly payments over two years, we can use the formula for the monthly payment on an installment loan:

\[
M = P \frac{r(1 + r)^n}{(1 + r)^n - 1}
\]

Where:
- \( M \) is the monthly payment
- \( P \) is the principal amount (the loan amount)
- \( r \) is the monthly interest rate (annual interest rate divided by 12)
- \( n \) is the number of payments (loan term in months)

Given:
- \( P = 3500 \)
- Annual interest rate = 8%, so the monthly interest rate \( r = \frac{0.08}{12} = \frac{0.08}{12} = 0.0066667 \)
- Loan term = 2 years = 24 months, so \( n = 24 \)

Now we can plug these values into the formula to calculate the monthly payment \( M \):

\[
M = 3500 \frac{0.0066667(1 + 0.0066667)^{24}}{(1 + 0.0066667)^{24} - 1}
\]

Calculating \( (1 + 0.0066667)^{24} \):

\[
(1 + 0.0066667)^{24} \approx 1.170187
\]

Now, substituting into the equation for \( M \):

\[
M = 3500 \frac{0.0066667 \times 1.170187}{1.170187 - 1}
\]
\[
M = 3500 \frac{0.007813\ldots}{0.170187} \approx 3500 \times 0.045973
\]
\[
M \approx 161.91
\]

Now calculating the total payback over two years:

\[
\text{Total Payback} = M \times n = 161.91 \times 24 \approx 3885.84
\]

So, the total payback for the loan is approximately **$3,885.84**.

Thus, your answer of **$3,815.28** is not correct; the correct total payback is around **$3,885.84**.