Question

OOO You need some money today and one of your friend agrees to loan you the money you need only if you make payments of $100 a month for the next eight months. In addition, he requires that the first payment be paid today. He will charge you 1.5 percent interest per month. How much money are you borrowing? APPROX. $770 APPROX $740 APPROX $750 APPROX. $760

Answer 1

Solution :

As per the information given in the question we have

Monthly amount Payable = $ 100 ; Rate of interest per month = 1.5 % ; No. of monthly payments = 8

The amount of borrowing will be equal to the present value of monthly payments with the first payment due today:

The formula for calculating the present value of monthly payments with the first payment due today:

PV = A + [ A* [ ( 1 - ( 1 / ( 1 + r ) ^{( n - 1 )} )) / r ] ]

Where

PV = Present value of monthly payments = Amount of Borrowing   ;

A = Monthly Payment   ;     r = rate of interest per month ;     n = no. of months

As per the information given in the question we have

r = 1.5 % = 0.015   ; n = 8 months   ; A = $ 100

Applying the above information in the formula we have

= $ 100 + [ $ 100 * [ ( 1 - ( 1 / ( 1 + 0.015 ) ^{( 8 – 1 )} )) / 0.015 ] ]

= $ 100 + [ $ 100 * [ ( 1 - ( 1 / ( 1.015 ) ^{( 7 )} )) / 0.015 ] ]

= $ 100 + [ $ 100 * [ ( 1 - ( 1 / 1.109845 )) / 0.015 ] ]

= $ 100 + [ $ 100 * [ ( 1 – 0.901027 ) / 0.015 ] ]

= $ 100 + [ $ 100 * [ 0.098973 / 0.015 ] ]

= $ 100 + [ $ 100 * 6.598214 ]

= $ 100 + $ 659.8214

= $ 759.8214

= Approx. $ 760 ( when rounded off to the nearest whole number )

Thus the amount of borrowing assuming the first payment is due today = $ 760

Thus the solution is Approx .760

Note: The value of ( 1.015 ) ⁷   is calculated using the Excel formula =POWER(Number,Power)

=POWER(1.015,7) = 1.109845