Question

A couple secures a 30 -year loan of $ 100,000 at 9 3/4% per year, compounded monthly, to buy a house. What total amount will they pay over the 30 -year period?

Answer 1

The couple will pay a total of $549,319.39 over the 30-year period.

Step-by-step explanation:

To find the total amount paid over the 30-year period, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the total amount paid, P is the principal amount (loan amount), r is the annual interest rate (9 3/4% = 0.0975), n is the number of times interest is compounded per year (monthly compounding means n = 12), and t is the number of years (30). Plugging in the values, we get A = $100,000(1 + 0.0975/12)^(12*30). Calculating this expression gives us approximately $549,319.39. Therefore, the couple will pay a total of $549,319.39 over the 30-year period.