Question

Kenneth has $1,000,000 in his investment account now (i.e. Year 0). He has decided to save $100,000 at the end of Year 1, $103,000 at the end of Year 2, $106,090 at the end of Year 3, and so on (i.e. increasing by around 3% each year) until the end of year 20. What is the total amount that Kenneth will have accumulated at the end of year 20 assuming that the annual rate of return is 10%?

Answer 1

Future worth of geometric series = A * [(1+i)^n - (1+g)^n] / (i - g)

Future worth of investment savings = 100000 * [(1+0.1)^20 - (1+0.03)^20] / (0.1 - 0.03)

= 100000 * [(1.1)^20 - (1.03)^20] / (0.07)

= 100000 * 70.30555307

= 7030555.31

Total future worth of investment account = 1000000 * (1+0.1)^20 + 7030555.31

= 1000000 * (1.1)^20 + 7030555.31

= 1000000 * 6.727499949 + 7030555.31

= 6727499.95 + 7030555.31

= 13758055.26