Answer:
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
