Question

An amount of $40,000 is borrowed for 6 years at 6.5% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?

Answer 1

The total amount to be repaid on a $40,000 loan with an annual compound interest rate of 6.5% over 6 years is $56,740.76.

Step-by-step explanation:

To calculate the amount that must be paid back on a loan of $40,000 with an annual compound interest rate of 6.5% over a period of 6 years, the formula for compound interest can be used:

A = P(1 + r/n)^(nt)

Where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for, in years.

In this case, P = $40,000, r = 6.5% or 0.065, n = 1 (since it is compounded annually), and t = 6. Plugging these values into the formula gives us:

A = $40,000(1 + 0.065/1)^(1*6)

A = $40,000(1 + 0.065)^6

A = $40,000(1.065)^6

A = $40,000 * 1.418519

A = $56,740.76

Therefore, the total amount that must be paid back at the end of the 6-year period is $56,740.76.