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

in Calculus Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

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.

by Top Rated User (717k points)

Related questions

Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
84,493 questions
89,413 answers
1,998 comments
8,094 users