Question

Which formula do I use to solve the following? Future Value, Future Value Ordinary Annuity, Future Value Annuity Due, Present Value, Present Value Ordinary Annuity, or Present Value Annuity Due?

13. Two investors- Investor "C" starts investing $400 a month at the beginning of each month at age 31 to age 70 (40 years) earning 7% per year. Investor "D" invests $4,800 a year at the beginning of each year at age 22 to age 33 (12 years) earning 7% a year. Then lets the amount of money at age 34 compound at 7% until age 70 (37 Years). Which investor made the most amount of money? Investor "C" who invested $192,000 ($400 a month for 40 years), or Investor "D" who invested $57,600 ($4,800 a year for 12 years)

Answer 1

The Future value annuity due and the future value formula will be used.

Total amount in the account of Investor C = (1+0.5833%) + 400[{(1+0.5833%)⁴⁸⁰ – 1}/0.5833%]

= $1,056,092.03

Total amount in the account of Investor D at the age 34

= (1+0.07)*4,800[{(1+0.07)¹²-1}/0.07]

= $91,875.09

Amount at the age 70 = 91,875.09*(1.07)³⁷

= $1,123,045.96

Hence, investor D made most money