Question

1. George and Sarah each invest $1,500 today. George is more conservative and invests his money in an account that is expected to earn 5% a year. Sarah is an aggressive investor and invests her money in an account that is expected to earn 18% a year. Assume George and Sarah each earns their expected rates of return. After 100 months, how much more money will Sarah have than George?

Answer 1

Amount received by George

Amount Invested = $1500

Interest rate per annum = 5%

Interest rate per month = 5/12 = 0.42%= 0.0042

Period of payment of interest = 100 times

Applying annuity formula

Future Value = 1500 *[(1+0.0042)¹⁰⁰-1] / 0.0042

Using Scientific Calculator, we get

Future Value = 1500 *[1.5206-1] / 0.0042

Future Value = 1500 *[0.5206/0.0042]

Future Value = 1500 *[123.9524]

Future Value = $ 185,928.60 i.e. the amount received by George at the end of 100 months

Similarly, in case of Sara

Amount Invested = $1500

Interest rate per annum = 18%

Interest rate per month = 18/12 = 1.5%= 0.015

Period of payment of interest = 100 times

Applying annuity formula

Future Value = 1500 *[(1+0.015)¹⁰⁰-1] / 0.015

Using Scientific Calculator, we get

Future Value = 1500 *[4.4320-1] / 0.015

Future Value = 1500 *[3.4320/0.015]

Future Value = 1500 *[228.8]

Future Value = $ 343,200 i.e. the amount received by Sarah at the end of 100 months

After 100 Sarah will have (343200-185928.60) $ 157271.40 more than George