Question

Lakeynn is planning to build a home for $400 000. She has 10% of the balance saved, and the rest she plans on financing through a construction loan from a bank. The loan is over a 15-year term at an interest rate of 4%.

Assuming yearly compounding interest, how much interest will Lakeynn have paid on the loan at the end of 15 years?

Answer 1

$231,780.48

Explanation:

To calculate the interest paid on the loan at the end of 15 years, we need to first find out how much Lakeynn plans to borrow from the bank, and then calculate the interest on that loan amount over the 15-year term.

Lakeynn plans to build a home for $400,000, and she already has 10% of the balance saved. So, the amount she plans to borrow from the bank is:

Loan amount = Total cost of home - Amount saved

Loan amount = $400,000 - (0.10 * $400,000)

Loan amount = $400,000 - $40,000

Loan amount = $360,000

Now, we can calculate the interest using the formula for compound interest:

Interest = Principal * (1 + (Annual Interest Rate))^Number of Years - Principal

Where:

Principal = Loan amount

Annual Interest Rate = 4% (0.04 as a decimal)

Number of Years = 15

Interest = $360,000 * (1 + 0.04)^15 - $360,000

Interest = $360,000 * (1.04)^15 - $360,000

Now, let's calculate the value of (1.04)^15:

(1.04)^15 ≈ 1.643618

Interest = $360,000 * 1.643618 - $360,000

Interest = $591,780.48 - $360,000

Interest = $231,780.48

So, Lakeynn will have paid approximately $231,780.48 in interest on the loan at the end of 15 years.