Question

suppose that $2000 is loaned at a rate of 9.5%, compounded quarterly. suming that no payments are made, find the amount owed after 5 ars. not round any intermediate computations, and round your answer t e nearest cent.

Answer 1

Rounding this to the nearest cent, the amount owed after 5 years is approximately $3102.65.

Explanation:

To calculate the amount owed after 5 years, we can use the formula for compound interest:

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

Where:

A = the final amount (amount owed)

P = the principal amount (initial loan)

r = the annual interest rate (in decimal form)

n = the number of times interest is compounded per year

t = the number of years

Given:

P = $2000

r = 9.5% = 0.095 (decimal form)

n = 4 (compounded quarterly)

t = 5 years

Plugging these values into the formula, we get:

A = 2000(1 + 0.095/4)^(4*5)

Calculating this expression gives us:

A ≈ $2000(1.02375)^(20)

A ≈ $2000(1.55132625)

A ≈ $3102.65

Rounding this to the nearest cent, the amount owed after 5 years is approximately $3102.65.