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Ahmet has a loan with an effective interest rate of 8% per annum. He makes payments...

Ahmet has a loan with an effective interest rate of 8% per annum. He makes
payments at the end of each year for 25 years. The first payment is 100, and each
subsequent payment increases by 20 per year. Calculate the original loan amount.
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Answer #1

The payment series can be broken down into two series:

Series 1: Payment of 100 for 25 years

Present value=Present value of ordinary annuity=payment/rate*(1-1/(1+rate)^n)=100/8%*(1-1/1.08^25)=1067.477619

Series 2: Arithmetic gradient of 20

Present value given as P is calculated using below formula

P=20/(8%*1.08^25)*((1.08^25-1)/0.08-25)=1756.082141

Total present value=Present value of first series+Present value of second series=1067.477619+1756.082141=2823.55976

Hence, loan amount=2823.55976

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