Question

A homeowner is using a personal loan to borrow $18,000 to replace the roof. the loan offers the option of making no payments for the first 12 months, during which the interest is compounded monthly at an annual rate of 4.5%. what is the total account balance at the end of the year?

Answer 1

The total account balance at the end of the year is $18,067.50.

Step-by-step explanation:

To calculate the total account balance at the end of the year, we need to consider the compounding interest on the loan. The loan amount is $18,000 and the annual interest rate is 4.5%. Since the interest is compounded monthly, we need to divide the annual interest rate by 12 and calculate the monthly interest rate. The monthly interest rate is 4.5% / 12 = 0.375%.

Let's calculate the total account balance at the end of the year:

First, we calculate the interest accrued over the 12-month period. 0.375% of $18,000 equals $67.50.

Next, we add the interest to the loan amount. $18,000 + $67.50 equals $18,067.50.

The total account balance at the end of the year is $18,067.50.

Answer 2

The total account balance at the end of the year is approximately $18,602.30.

Step-by-step explanation:

To calculate the total account balance at the end of the year, we need to consider the interest that is compounded monthly for the first 12 months. The loan amount is $18,000 and the annual interest rate is 4.5%. To calculate the monthly interest rate, we divide the annual interest rate by 12. So, the monthly interest rate is 4.5% / 12 = 0.375%.

Since the interest is compounded monthly, we can use the formula for compound interest to find the total account balance:

A = P(1+r)^n

Where:

A is the total account balance,

P is the loan amount,

r is the monthly interest rate, and

n is the number of compounding periods.

Plugging in the values, we get:

A = $18,000(1+0.00375)^12

Calculating this value, we get:

A ≈ $18,602.30

Therefore, the total account balance at the end of the year is approximately $18,602.30.