Question

Ms. Chambers applied for a home improvement loan that has an annual interest rate of 6%, compounded monthly. The following expression represents the total amount that she will spend to pay off the loan in t years.

What is the exponential expression in the form (b)c that reveals the monthly interest rate on the loan?

Answer 1

B.
`120,000(1.005)^(12t)`

Explanation:

We are given that,

The expression representing the amount of the loan with 6% interest rate is,

Loan amount =
`120,000(1.06)^t` =
`120,000(1+0.06)^t`

Now, we want to find the amount which represents the loan being compounded monthly.

Thus, we have that,

Loan amount compounded monthly =
`120,000(1+(0.06)/(12))^(12t)`

i.e. Loan amount compounded monthly =
`120,000(1+0.005)^(12t)`

i.e. Loan amount compounded monthly =
`120,000(1.005)^(12t)`

Hence, the expression representing the monthly interest rate on the loan is
`120,000(1.005)^(12t)`.

So, option B is correct.