Question

Suppose that $2000 is loaned at a rate of 11.5%, compounded annually. Assuming that no payments are made, find the amount owed after 8 years.

Do not round any intermediate computations, and round your answer to the nearest cent.

Answer 1

After 8 years, the amount owed would be approximately $3959.79. Rounded to the nearest cent, the amount owed is $3959.80.

Explanation:

To calculate the amount owed after 8 years with a loan of $2000 at an annual interest rate of 11.5%, compounded annually, we can use the formula for compound interest:A = P(1 + r/n)^(nt)Where:

A is the final amount owed

P is the principal amount (initial loan)

r is the annual interest rate (as a decimal)

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

t is the number of yearsIn this case:

P = $2000

r = 11.5% = 0.115 (as a decimal)

n = 1 (compounded annually)

t = 8 yearsSubstituting the values into the formula:A = $2000(1 + 0.115/1)^(1*8)

= $2000(1.115)^8

≈ $2000(1.979894357)

≈ $3959.79