Question

A borrower had a loan of $ 60 comma 000.00 at 4 % compounded annually comma with 8 annual payments. Suppose the borrower paid off the loan after 4 years. Calculate the amount needed to pay off the loan. The amount needed to pay off this loan after 4 years is ​$.

Answer 1

Answer:

The amount needed to pay off the loan after 4 years is $70,192

Step-by-step explanation:

When interest is compounded annually, total amount A after t years is given by:

$A = P(1 + r)^{t}$

where P is the initial amount (principal), r is the rate and t is time in years.

From the question:

P = $60,000

r = 4% = 0.04

t = 4

$A = 60000(1 + 0.04)^{4} \\A = 60000(1.04)^{4}\\A = 60000 * 1.16985856\\A = 70191.5136\\A = 70192$

The amount needed to pay off the loan after 4 years is $70,192

If we divide the amount by four, we will get the amount that is paid yearly (70192/4 = 17548). $17,548 is paid yearly.