Welcome to the hotseat. We've prepared a guide if you'd like to read more about how it works.

Question 12.17 ActEd (FV problem)

+2 votes
66 views
asked Nov 10, 2016 in BUS 2016H - Financial Mathematics by Palie (280 points)

A woman pays 5% of her annual salary of R30 000 into a fund at the start of each of the next 15 years. If the fund is expected to earn 8% interest each year and her salary is expected to increase by 6% each year, calculate the approximate amount of the fund at the end of the 15 years. 


PV=1500 + 1500*(1.06/1.08)^1 + 1500*(1.06/1.08)^2 + ... + 1500*(1.06/1.08)^14

(1/1+j)=(1.06/1.08)

I got a new rate of j=0.01887..

I then used this j to calculate a future value for this annuity... Got the wrong answer :(

The memo states that I must first get a PV using the j, then calculate the FV using 8%. Why is this so? Why take the "long route"?  

1 Answer

+1 vote
answered Nov 10, 2016 by simon_rigby (4,220 points)
selected Nov 15, 2016 by Richard van Gysen
 
Best answer

Try to write out the equation of value:

$$FV = [30000(0.05)]\times[(1.08)^{15} + (1.06)^1(1.08)^{14} + (1.06)^2(1.08)^{13} + \dots + (1.06)^{14}(1.08)^1]$$

and you should see why your method doesn't work.

...