Question

cheyenne took out a 30 year loan for $350,000 at 2.9% interest, compounded monthly. if her monthly payment on the loan will remain $1456.80 for the life of the loan, how much will cheyenne have paid in interest once the loan is paid off?

A. $ 524,448.00
B. $360,150.00
C. $350,000.00
D. $174,448.00

Answer 1

To find out how much Cheyenne will have paid in interest by the end of the loan, we can use the following formula:

\[
\text{Total Payment} = \text{Monthly Payment} \times \text{Number of Payments}
\]

1. **Calculate the total number of payments**:
Since it is a 30-year loan with monthly payments, the total number of payments will be:
\[
\text{Total Payments} = 30 \text{ years} \times 12 \text{ months/year} = 360 \text{ payments}
\]

2. **Calculate the total amount paid over the life of the loan**:
We know that Cheyenne's monthly payment is $1456.80, so the total amount paid over the life of the loan is:
\[
\text{Total Payment} = 1456.80 \times 360 = 524,448.00
\]

3. **Calculate the total amount paid in interest**:
To find the total interest paid, we subtract the principal (the initial loan amount) from the total payment:
\[
\text{Interest Paid} = \text{Total Payment} - \text{Principal}
\]
\[
\text{Interest Paid} = 524,448.00 - 350,000.00 = 174,448.00
\]

Therefore, Cheyenne will have paid **$174,448.00** in interest once the loan is paid off.

So, the answer is:

**D. $174,448.00**