S.O.S. Mathematics CyberBoard

Hi,

I dont know how to calculate the Present Value of an annuity of $50 received at the end of each year for 10 years, with the first payment to be received at the end of the 6th year. Assuming a discount rate of 8%

Could somebody explain to me how this works? what happens for the first 5 years? nothing is received?

Any clarity would be much appreciated

Thank you all

Yes, no payment in the first 5 years. Payment at the end of 6th, 7th, ...., 15th year.

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x = PV of $50 annuity, n = 10
PV now = PV of x, n = 5

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I'm not prejudiced...I hate everybody equally!

Thank you Denis,

I dont quite follow. So this annuity of $50 received at the end of each year for 10 years, with the first payment to be received at the end of the 6th year.

First, we calculate the present value of the annuity over 10 years
discounted at 8%

PV(n=10) = $50*(1-[1.08]^-10)/0.08 = $355.50

But then, the first payment doesnt come in until the end of the 6th year. So what do we do next?

Perhaps this'll make it clear:

(*2) : this is the required amount at end of year#5 to permit annual
withdrawals of 50 from year#6 to year#15 : 10 years.
(your 355.50 is a typo, I guess?)

We next need the PV of this 335.50: 335.50 / 1.08^5 = 228.34 (*1).

S'that nuff?

Btw, you can combine the 2 calculations:
[$50*(1 - 1.08^-10) / .08] / 1.08^5 = 228.34

_________________
I'm not prejudiced...I hate everybody equally!