Question

Part 1: You are a diligent saver who started with nothing but manages to put away $250 at the end of each month, owed largely to your total abstinence from avocado toast and fancy coffee. If you keep up this habit for a total of 15 years with your savings growing at 7.50% (monthly compounded), what nominal wealth can you look forward to in your investment account at the end of your savings efforts? $ Part 2: Allowing for an inflation rate (monthly compounded) of 1.00%, what is the real rate of return per month (HINT: you should use the per-month rates to directly compute a per-month real rate here and use it as input in the next part)? % Part 3: Assuming that your monthly savings amount from the first part keeps pace with inflation, what amount will you have saved in real terms? $ Bonus question: Alternatively, assuming that you do not increase your monthly savings amount with inflation over the accumulation period, what amount in real terms will you have saved then? $

Answer 1

Part (1):

Nominal wealth at the end of 15 years= $82,778.07 calculated as the future value of annuity, as follows:

Part (2):

Real rate of return= (R-i)/(1+i)

Where R= Nominal interest rate given as 7.5% 0r 0.075) and i= inflation rate (given as 1% or 0.01)

Substituting the values, Real Rate of Return = (0.075-0.01)/(1+0.01)

=0.065/1.01 = 6.435644% .

Monthly real rate of return= 6.435644%/12 = 0.536304%

Part (3):

In case the monthly savings was increased with inflation rate, amount saved in 15 years is the future value of growing annuity with the real interest rate as in part (2) and growth rate of 1% per year compounded monthly.

The future value is   $ 80,423.14 as follows:

Alternatively, if the monthly savings is not increased with inflation, amount that could have been saved in 15 years, in real terms is the FV of annuity at the real interest rate as above.

The FV= $75,467.21 calculated as follows: