Tabitha had to pay her friend $800, 3 months ago and he has to pay $650...

Tabitha had to pay her friend $800, 3 months ago and he has to pay $650 in 3 months. If her friend was charging her an interest rate of 0.40% per month, what single payment would settle both payments today?

Expert Solution

PV and future value of single sum are related as:

FV = PV x (1+r) n

PV = FV /(1+r) n

r = Periodic rate = 0.4 % p.m.

n = Number of periods = 3 months

Total current settlement amount = PV of $ 800 + PV of $ 650

= $ 800 x (1+ 0.004)3 + $ 650 / (1+ 0.004)3

= $ 800 x (1.004)3 + $ 650 / (1.004)3

= $ 800 x 1.012048064 + $ 650 / 1.012048064

= $ 809.6384512 + $ 642.2619864821

= $ 1,451.9004376821 or $ 1,451.90

Tabitha can settle both the payment with $ 1,451.90 today.

jeff jeffy answered 1 year ago

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