Math Problem Help

Question

What annual compound interest rate is required for the debt of a compound interest loan to grow by 42% in 14 years?

Round your answer to the nearest tenth of a percent. 

Answer 1

Let D = (A+I) = Amount loaned + Interest = total debt, t = time (14 years) and r = interest rate.

D=1.42 which is 42% greater than the original loaned amount A

1.42A = A(1+r)^t

Divide both sides by A to get 1.42 = (1+r)^t ==> 1.42 = (1+r)¹⁴

Take the 14th root of both sides to get 1.42^1/14 = 1+r ==> 1.42^0.07142871 = 1+r

Using a scientific calculator yields 1.02536229 = 1+r, so r = 0.02536 ~ 2.5%.

Test this answer by selecting A = $2222 (original loan).

A+I = A(1+0.02536)¹⁴

A+I = 2222(1.02536)¹⁴

A+I = 2222*1.41994 = $3155.00 to nearest dollar

Interest I = 3155 - 2222 = $933 which adds ~ 42% debt to the original loan.