If you buy a cup of coffee that costs 275 every day what wou

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).

Solution

Monthly (nominal) interest rate = 6%/12 = 0.5%

Monthly investment = $2.75 x 30 = $82.5 (Assuming average 30 days per month)

Number of years = 40

Number of months = 40 x 12 = 480

Accumulated future value ($) = 82.5 x F/A*0.5%, 480) = 82.5 x 1,991.4907** = 164,297.99

**F/A(r%, N) = [(1 + r)^N - 1] / r

F/A(0.5%, 480) = [(1.005)⁴⁸⁰ - 1] / 0.005 = (10.9575 - 1) / 0.005 = 9.9575 / 0.005 = 1,991.4907