Question

Tabitha had to pay her friend $1,200, 5 months ago and he has to pay $450 in 2 months. If her friend was charging her an interest rate of 0.70% per month, what single payment would settle both payments today?

Answer 1

Future value formula:

FV = PV x (1+r)ⁿ

Present value Formula:

PV = FV / (1+r)ⁿ

Given,

r = 0.7% or 0.007

n = 5 months for $1,200 and 2 months for $450

Therefore single payment would settle both debts today calculated as follows:

We want to pay both debts today. So we have to calculate the present values of the amounts.

Total settlement amount today = PV of $1,200 + PV of $450

= [$1,200 x (1+0.007)⁵] + [$450 / (1+0.007)²]

= [$1,200 x (1.007)⁵] + [$450 / (1.007)²]

= ($1,200 x 1.035493) + ($450 / 1.014049)

= $1,242.59 + $443.77

= $1,686.36

single payment would settle both debts today is $1,686.36

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