Question

If you buy a cup of coffee that costs $2.75 every day, what would happen if you instead save it and invest (on a monthly basis) into a 50/50 mix of low cost stock index fund and high-quality bonds for an inflation adjusted return of 6% a year. How much would you accumulate by the time you retire?

Note: you plan to retire at age 65, and current age is 25.

The monthly cost is your monthly investment (at 6% per year, but you can use 0.5% per month).

Answer 1

SAVING PER DAY = 2.75

SAVING PER MONTH = 2.75 X 30 = 82.5

TOTAL INVESTMENT PERIOD = 65-25 = 40 YEARS

WE HAVE TO CALCULATE FUTURE VALUE OF ALL SAVINGS

FUTURE VALUE OF ANNUITY = A* [(1/i) (1+i)ⁿ -1)

i = 0.5% PER MONTH = 0.005, n = TOTAL NO OF PERIODS = 40 X 12 = 480

FUTURE VALUE OF ANNUITY = 82.5* [(1/0.005) (1+0.005)⁴⁸⁰ -1) ]

FUTURE VALUE OF ANNUITY = 82.5* [(200) (10.9575 -1)]

FUTURE VALUE OF ANNUITY = 82.5* [ 1991.5] = 164298.75 ANSWER

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