You just received a loan offer from Mako Loans. The company is offering you $8,000 at 6.25 percent interest. The monthly payment is only $200. If you accept this offer, how long will it take you to pay off the loan? a) 4.3 years b) 5.26 years . c) 3.75 years d) 6.05 years e) 4.099 years

c) 3.75 years

Explanation:

A fix Payment for a specified period of time is called annuity. The discounting of these payment on a specified rate is known as present value of annuity. The value of the annuity is also determined by the present value of annuity payment.

Formula for Present value of annuity is as follow

PV of annuity = P x [ ( 1- ( 1+ r )^-n ) / r ]

Where

P = Monthly Payment = $200

r = rate of interest = 6.25%

PV = Loan amount = $8,000

As we already have the present value of annuity we need to calculate the rate of return.

$8,000 = $200 x [ ( 1- ( 1+ 6.25%/12 )^-n ) / 0.0625/12 ]

$8,000 / $200 = [ ( 1- ( 1.0052 )^-n ) / 0.0052 ]

40 x 0.0052 = 1- ( 1.0052 )^-n

0.028 = 1 - 1.0052^-n

0.028 - 1 = - 1.0052^-n

-0.792 = - 1.0052^-n

0.792 = 1/1.0052^n

1.0052^n = 1/0.792

1.0052^n = 1.2626

n log 1.0052 = log 1.2626

n = log 1.2626 / log 1.0052

n = 44.96 months

n = 44.96 / 12 = 3.75

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