Your financial planning client wishes to have investment savings in 20 years tha

Question

Your financial planning client wishes to have investment savings in 20 years that will provide $1.0 million dollars of purchasing power, measured in today's (real) dollars. The current balance of the client's investment account is $75,000. Nominal investment rates of return are 9.2% per annum, the expected inflation rate is 4% per annum, and the real rate of return is 5% per annum. In today’s (real) dollars, how much must the client save per month starting at the end of the current month to accomplish this goal, given these rates of return? Assume monthly compounding.

Explanation / Answer

This is a typical equal installments problem where we have to find PMT

Here PV is given as 75,000,

FV as 1,000,000

Rate is 9.2%

number of years of investments are 20

SInce FV should be 1,000,000 in today's rate, we have to adjust FV as follows

First find the current value using real rate of return of 5%,

so PV = PV(5%/12,20*12,0,-1000000,0) = 368,655.53

Now find the FV of this using the rate as (5+4) = 9% which is real + inflation rate

FV = FV(9%/12,20*12,0,-368655.53,0)=2,215,240.83

So PMT can be calculated in an excel as follows

=PMT(9.2%/12,20*12,-75000,2215240.83,0) = 2,548.94

Interest rate and number of years are adjusted by 12, because investment is compunded monthly

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