Question

Derek will deposit $4,425.00 per year for 25.00 years into an account that earns 15.00%, The first deposit is made next year. How much will be in the account 43.00 years from today?

Derek will deposit $717.00 per year into an account starting today and ending in year 9.00. The account that earns 9.00%. How much will be in the account 9.0 years from today?

Derek will deposit $4,818.00 per year for 29.00 years into an account that earns 13.00%, The first deposit is made next year. How much will be in the account 40.00 years from today?

Answer 1

Answer to the first question

• First we need to find out future value annuity of $4425 for 25 years at 15%.
  The future value annuity table gives the annuity factor for the 25th year at 15% as 212.7930.
  So, the amount will be $941,609.03, being $4425 x 212.7930, after all deposits are made
  The same can be obtained from excel formula: =FV(15%,25,-4425), and the result would be $941,609.10 (only negligible difference in rounding).
• Now, we need to apply 15% compounding per year for the remaining (42-25) years. [It's 42 and not 43 because investing starts an year later, but 43 years is from TODAY].
  That will be 1.15¹⁷ x $941,609.03 = $10,132,903.36. [There will be rounding difference of a few dollars if you round up intermediate calculations]

Answer to the second question

• We need to apply Future value annuity of 9% at the 9th year. That is 13.0210.
  So the amount will be $717 x 13.0210 = $7,336.06

Answer to the third question

• Future value annuity table of 13% at the 29th year gives the factor as 258.5834.
  So the amount after all deposits are made will be $4818 x 258.5834 = $1,245,854.82
• Now we need to apply 13% compounding per year for remaining (39-29) years.
  That will be 1.13¹⁰ x 1,245,854.82 = $4,229,178.77. [There will be rounding difference of a few dollars if you round up intermediate calculations]

Please note that there will be rounding differences always. The difference can be negligible (few cents) to few dollars if intermediate roundings are done.

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