Tom Bond borrowed $6200 at 5 1/2% for 3 yrs compounded annually. What is the compound amount of the loan..

Question

Tom Bond borrowed $6200 at 5 1/2% (fraction) for 3 yrs compounded annually. What is the compound amount of the loan and how much interest will he pay on the loan?

 

Compound amount? (round to the nearest cent as needed)

Compound interest? (round to the nearest cent as needed)

Answer 1

In 1 year, you add 5.5% of what you had a year ago (P).

So after the first year, you have:

 Maturity, M1 = P + (5.5/100)*P  = P(1+0.055)

 

After the 2nd year, 

M₂ = M₁ + (5.5/100)*M₁ =  M₁(1+0.055) = P(1+0.055)(1+0.055)

 

After 3rd year,

M₃ = M₂ + (5.5/100)*M₂ = M₂(1+0.055) = P(1+0.055)(1+0.055)(1+0.055)

 

There is a noticeable trend for compound interests:

 

Compound Amount, A = P(1+r)^t

where r is the rate per year, and t is the number of years.

 

Straightforward answer:

 

Compound Amount, A = 6200(1+0.055)³

                                A = $7280.30

 

Compound Interest = A  - P 

                                = $7280.30 - $6200.00

                                = $1080.30