# Accumulation question.

• Jan 13th 2011, 03:34 AM
DCU
Accumulation question.
An investor is to receive a series of annual payments for a term of 15 years in which payments are
increased by 2.5% compound each year to allow for inflation. The first payment is to be €14,400 on 1 January 2011. Find the accumulated value of the annuity payments as at 1 January 2031 if the investor achieves an effective rate of return 3.5% per annum effective.
• Jan 14th 2011, 07:46 PM
Wilmer
Quote:

Originally Posted by DCU
An investor is to receive a series of annual payments for a term of 15 years in which payments are
increased by 2.5% compound each year to allow for inflation. The first payment is to be €14,400 on 1 January 2011. Find the accumulated value of the annuity payments as at 1 January 2031 if the investor achieves an effective rate of return 3.5% per annum effective.

A bit hard to follow: 2011 to 2031 is not 15 years...
anyway, I'll assume 15 years, 1st deposit end of 1st year:
n = 15
p = 14400
x = 1 + .025
y = 1 + .035

F = p(y^n - x^n) / (y - x) = 14400(1.035^15 - 1.025^15) / (1.035 - 1.025) = 326952.9565...

Account will look like:
Code:

```YEAR    PAYMENT    INTEREST    BALANCE  0                                .00  1    14400.00        .00  14400.00  2    14760.00      504.00  29664.00  3    15129.00    1038.24  45831.24 .... 15    20346.82    10368.32  326952.96```
• Jan 15th 2011, 03:44 AM
DCU
Sorry, I figured it out a few days ago. The annuity is paid over 15 years so you get the accumulation to 15 but you also have to find out what this is worth 5 years later, ie in 2031, without any payments, just interest. This was my equation of value:

F = 14,400(y)(( 1 - (x/y)^15)/(1- (x/y)))
This is the value after all of the annuity is paid after 15 years
Then, we must find out what it accumulates to 5 years later which is simply:
A = F(y)^5

Thanks for the help though :D

I'm using the notation you were using, x = 1 + .025
y = 1+.035