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chapter 12

M

mayughodake9

Member
Q.12.17
To provide for her retirement a woman has decided to pay 5% of her annual salary,currently £30,000 per annum, into a special savings account 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.

yearly amount = 30000*0.05=1500

i=8%
j=6%

i'= [1.08/1.06]-1 = 0.01886

acc. value = 1500* [(1+0.01886)^15-1]/(0.01886/1.1886)

= 26214

bt in solution ans is different. what is my mistake?
 
It turns out that you're accumulating at the wrong interest rate.

If something's not working (or unusual) go back to first principles to work out what's going on.

Here, the present value of the payments is:

1500(1+1.06v+1.06^2*v^2+....)

Using your adjusted interest rate of i' = 0.0188679..., the present value of these payments can be expressed as:

1500* a-due_15 @i'

But then the accumulation forward to time 15 must be done at 8% (as that is the true interest rate over the period). So the accumulated value is:

1500*(a-due_15 @i')*(1.08)^15

Using that, I get the accurate answer stated of £62,824.
 
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