# Math Help - Accumulation question.

1. ## 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.

2. 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

3. 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

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