Question

if you make the following deposits ( payments)

: EOY 0 payment is 9600 $, EOY 1-10 payments are 12000 $ ( 10 equal payments), where : EOY : End of year.

Assuming that interest rate is 10% per year compounded annually, what would be the equivalent present amount to these payments.

Answer 1

Lets First Calculate Present value of Periodic payment

Present Value of a periodic payment is given by :

PV = (P/r)(1 - 1/(1 + r)ⁿ)

where PV = Present value , P = periodic payment = 12000, r = interest rate = 10% = 0.10 and n = time period = 10

=> PV = (12000/0.10)(1 - 1/(1 + 0.10)¹⁰)

Now, Lets Calculate Present value(PV) of EOY 0 payment which is that only

So, PV of EOY 0 is equal to 9600 only

Hence Net Present value = 9600 + (12000/0.10)(1 - 1/(1 + 0.10)¹⁰) = 83334.81

Hence, the equivalent present amount to these payments = $83334.81