Joe takes out a loan for educational training

Question

Joe takes out a loan for educational training. He borrows $15,000 at 4% interest. For each situation below, assuming he makes no payments, write a function to express how much he owes (L) after t years for each situation. Then, find the amount he owes for each situation after 4 years.

Part a

Interest is compounded quarterly

Part b

Interest is compounded monthly

Part c

Interest is compounded annually

Answer 1

Part a

compounded quarterly = 15000(1 + 4/100)^{1/4 of t} = 15000( 1 + 0·04)^{1/4 ×4} = $15600

Part b

compounded monthly = 15000( 1 + 4/100)^{1/12 of t} = 15000(1 +0·04)^1/12×4 = $15197·39

Part c

compounded annually = 15000( 1 + 4/100)^t = 15000( 1 + 0·04)⁴ = $ 17547·88.

Answer 2

A = 15000(1 + 0.04/4)^4t

A = 15000(1 + 0.04/12)^12t

A = 15000(1 + 0.04)^t

Substitute 4 for t in each equation and simplify.