Harrison and Sherrie are making decisions about their bank accounts. Harrison wants to deposit $200 as a principle amount, with an interest of 2% compounded quarterly. Sherrie wants to deposit $200 as the principle amount, with an interest of 4% compounded monthly. Explain which method results in more money after 2 years. Show all work.

Question

Mathematics

Brooklyn Gibson

16 July, 06:55

Harrison and Sherrie are making decisions about their bank accounts. Harrison wants to deposit $200 as a principle amount, with an interest of 2% compounded quarterly. Sherrie wants to deposit $200 as the principle amount, with an interest of 4% compounded monthly. Explain which method results in more money after 2 years. Show all work.

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Dorian Horne · Answer 1

We first solve for the effective interest rate by dividing the nominal rate by the number of time periods in a year, adding 1, and exponentiating to that number of time periods.

The effective interest rate for Harrison is (1+0.02/4) ^4 = 1.02015. After 2 years, his money will have grown to ($200) (1.02015) ^2 = $208.14.

The effective interest rate for Sherrie is (1+0.04/12) ^12 = 1.04074. After 2 years, her money will have grown to ($200) (1.04074) ^2 = $216.63.

Therefore, Sherrie will have more money than Harrison.