Question

Loan payments of $1725 due today, $510 due in 75 days, and $655 due in 323 days are to be combined into a single payment to be made 115 days from now. What is that single payment if money is worth 8.5% p.a. and the focal date is 115 days from now?

Answer 1

Following Loan payments are due:-

Loan Payment 1(LP1) due today = $1725

Loan Payment 2(LP2) due in 75 days = $510

Loan Payment 3(LP3) due in 323 days = $655

All the above payments are to be paid in a single payment on 115 days from now.

Lets take the Focal date as 115 days from now.

First, we will Compound Interest in LP1 and LP2 on Focal date as they are due before the focal date.

where, r = Interest rate = 8.5%

m = no of times compounding in a year = 365

n = Focal date = 115

Future Value = $1770.14 + $514.60

Future Value = $ 2284.74

So, Value of LP1 and LP2 on focal date is $2284.74

- Now, discounting LP3 back to Focal date:-

where, r = Interest rate = 8.5%

m = no of times compounding in a year = 365

n = Focal date = 115

Present Value = $625.10

So, Value of LP3 on focal date is $625.10

Total Value of all three loan payments on focal date = $2284.74 + $625.10 = $2909.84

So, the Single Payment is $2909.84

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