Question

An amount of 20,000 is borrowed for 7 years at 6% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?

Round your answer to the nearest dollar.

Answer 1

The total amount that needs to be paid back at the end of the 7-year period is approximately $28,370

Explanation:

To calculate the total amount that needs to be paid back after 7 years, we need to use the formula for compound interest:

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

Where:

A = the final amount (the amount to be paid back)

P = the principal amount (the initial loan amount)

r = the annual interest rate (in decimal form)

n = the number of times the interest is compounded per year

t = the number of years

In this case, the principal amount (P) is $20,000, the annual interest rate (r) is 6% (or 0.06 in decimal form), the number of times the interest is compounded per year (n) is 1 (since it is compounded annually), and the number of years (t) is 7.

Plugging in these values into the formula, we have:

A = 20000(1 + 0.06/1)^(1*7)

Simplifying the expression inside the parentheses:

A = 20000(1.06)^7

Calculating the value of (1.06)^7:

A = 20000(1.4185)

Multiplying 20000 by 1.4185:

A ≈ 28,370

Therefore, the total amount that needs to be paid back at the end of the 7-year period is approximately $28,370.

Have an excellent day :)