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

Answer:

B. $120,000(1.005)^{12t}$

Step-by-step 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 = $120,000(1+\frac{0.06}{12})^{12t}$

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.