Question

Suppose that 2000$ is loaned at a rate of 20% , compounded semiannually. Assuming that no payments are made, find the amount owed after 5 years.

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

Answer 1

$6,191.66

Explanation:

We can use the formula for compound interest to solve this problem:

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

where:

A = the amount owed after 5 years

P = the initial loan amount = $2000

r = the annual interest rate expressed as a decimal = 0.20

n = the number of times the interest is compounded per year = 2 (semiannually)

t = the number of years the loan is outstanding = 5

Plugging in these values, we get:

A = 2000(1 + 0.20/2)^(2*5)

= 2000(1.10)^10

≈ $6,191.66

Therefore, the amount owed after 5 years is approximately $6,191.66.