Juan and Michelle each have $800. Juan plans to invest $200 for each year of the next four years, while Michelle plans to invest all $800 now. Both accounts pay 3% annual interest compounded monthly.

Question

Full question

1. Juan and Michelle each have $800. Juan plans to invest $200 for each year of the next four years, while Michelle plans to invest all $800 now. Both accounts pay 3% annual interest compounded monthly. Will they have the same amount of money after four years? Explain why or why not.

please explain and show work

Answer 1

3% per annum is 3/12=¼% monthly.

Michelle’s $800 grows to 800×1.0025⁴⁸=$901.86 in 4 years (48 months).

Juan’s $800 grows:

$200 grows to $206.08 1st year, 1.0025¹²=1.030416 growth rate for 12 months.

Start of 2nd year: $406.08 grows to $418.43 by the end of 2nd year.

Start of 3rd year: $618.43 grows to $637.24 by the end of 3rd year.

Start of 4th year: $837.24 grows to $862.71 by the end of 4th year.

So Michelle gains more than Juan because the whole of the $800 was invested at the beginning so earned 4 years’ growth, whereas Juan only invested $200 for 4 years, $200 for 3 years, $200 for 2 years and $200 for 1 year.