InvestorQ : Is the impact of frequency of compounding the same for future value and for present value?
Abhi Yadav made post

Is the impact of frequency of compounding the same for future value and for present value?

Answer
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Abhisha Yadav answered.
1 year ago


Actually, it is the opposite. When frequency of compounding is increased, the future value benefits but the present value actually loses out. For the present value, a higher compounding frequency reduces the present value. This is because more compound interest is earned, which reduces the amount that must be saved today to be worth a specified sum in the future.

As an example, suppose that an investor has a target of Rs.100,000 in five years, and can invest in a bank account that pays an annual rate of interest of 6%. How much must the investor save today in order to reach this goal based on the following compounding frequencies?

Annual compounding

Semi-annual compounding

Monthly compounding

With annual compounding, t = 5, r = 6% and FV5 = Rs.100,000.

PV = FVt / (1+r)^t PV = 100,000 / (1+.06)^5 PV = 100,000 / 1.33823 PV = Rs.74,725.82

With semi-annual compounding, t = 10, r = 3% and FV10 = Rs.100,000.

PV = FVt / (1+r)^t PV = 100,000 / (1+.03)^10 PV = 100,000 / 1.34392 PV = Rs.74,409.39

With monthly compounding, t = 60, r = 0.5% and FV60 = Rs.100,000.

PV = FVt / (1+r)^t PV = 100,000 / (1+.005)^60 PV = 100,000 / 1.34885 PV = Rs.74,137.22

What do we see in the above illustration? As the frequency of compounding increases, the present value falls. But you must look at it differently. It means that you want to reach a fixed sum at a future date, then you need to save less today if you want to reach the same goal with more frequent compounding. That is the crux of time value.