Question

How long​ (in years) will it take Michael Garbin to pay off a ​$5000 loan with monthly payments of ​$156.49 if the​ add-on interest rate is 5.1​%?

Michael Garbin would take ___ years to pay off a ​$5000 loan amount.

Answer 1

This can be solved using the Present value of annuity formula

Present value of annuity is = P*(1-(1+r)^-n)/r

Present value of annuity is = Loan = $ 5,000/.

"r" is Monthly interest rate = 5.1%/12 = 0.4250%

"n" is No of months = ?

"P" is Monthly payment = $ 156.49/.

5000=156.49*(1-(1+0.004250)^-n)/0.00425

5000=156.49*(1-(1.004250)^-n)/0.00425

(1-(1.004250)^-n)=(5000/156.49)*0.00425

(1-(1.004250)^-n)=0.135791424

1.00425^-n=1-0.135791424

1.00425^-n=0.864208576

Using trial and error method, n is 34.41 months

It will take 34.41 months or 2.8675 years to pay off $ 5,000 loan