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**

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