Hi all, I have a question regarding to Chapter 12, Question 12.17. The question is like this: "To provide her with her retirement, a woman has decided to pay 5% of her annual salary, currently 30,000 p.a., into a special saving account at the start of each of the next 15 years. If the fund is expected to have 8% interest each year, her salary expected to increase 6% each year, calculate the approximate amount of the fund at the end of 15 years." The solution treats 6% as "inflation", 8% as "money rate of interest", and works out the "real interest rate", which is approximately 2%. I don't understand is that why we need to use this 2% to find present value first, then accumulate to 15 years later using 8% interest rate. In another word, why we use different interest rate to do present value and future value?
You can solve it by usual method i.e. PV by making a GP series and then AV by accumulating @8% pa. It will give the exact answer. But the qus. asks for approximate answer , so they have used approximate rate (see the pic below).
Thanks Baharti! I've got the same result as you, but I'm still a bit confused. Why we use 2% (or 1.88% exact) to find PV first, then use 8% to accumulate value in 15 years time? My first approach is to use 2% to find future value directly, and obviously it is not the right way to do it. I'm confused about why...
Because we have already considered the effect of growth of 6% in PV. So, we can just find AV using 8%. What I think if you accumulate it using 2% after finding the PV @2%, it would mean that you are cancelling the effect of growth we have used in PV i.e. you are doing (1.08/1.06)^15. It's not correct. And if you want to find AV directly then we don't have that approximate method to use in this case. (See the eq. in pic below) Since , now it is not in the form of 1.08ⁿ/1.06ⁿ.
Thank you, this really helps! To me the method of "2% find PV then 8% find AV" is more like a simplified version of this first principle equation you wrote. After finding the sum of this geometric sequence, the whole equation reduced down to "a due(15)@1.88% multiply by 1.08^15", and this makes sense to me. Cheers!
