Last year, you borrowed money from Cousin Vinnie and he agreed to a 25 percent interest...

Question

Question

Last year, you borrowed money from Cousin Vinnie and he agreed to a 25 percent interest rate per year. If you borrowed $250, and know you have to pay him in full exactly $488.28 (and make no other payments to him), what will be the total length of the loan?

Business Finance

0 0

Add a comment Transcribed image text

Answer 1

Answer #1

Formula for compound interest can be used to compute duration of loan.

A = P x (1 + r/m) ^mt

A = Future value of loan = $ 488.28

P = Principal = $ 250

r = Rate of interest = 25 % or 0.25 p.a.

m = No. of compounding in a year = 1 (supposed)

t = No. of years

Substituting the values in the above formula, we get:

$ 488.28 = $ 250 x (1+0.25) ^t

$ 488.28 / $ 250 = (1.25) ^t

1.95312 = (1.25) ^t

Taking log of both sides and solving for t, we get:

Log 1.95312 = t x log 1.25

0.29072892722 = t x 0.096910013

t = 0.29072892722 / 0.096910013

t = 2.99998852770766 or 3 years

Total length of the loan is 3 years.