# Math

Mary B deposits \$8500 into a savings account, compounded monthly at a nominal interest rate of 9 percent, as part of a savings plan that she would like to undertake in 5 years.
1) What is the effective interest rate per annum?
2) How much money would she have saved after 5 years?
3) Mary has an an emergency at the end of the second year after she had invested the money.She withdraws \$5000 How much money would she receive after 5 years?

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1. 1) The balance after one year with compounding is increased by a factor
(1 +(.09/12)^12 = (1.0075)^12 = 1.093807
The effective annual interest rate is therefore 9.3807%

2) 8500*(1.093807)^5 = \$ 13,308.29

3) After two years and withdrawing \$5000, she is left with
8500*(1.093807)^2 - 5000
= 10,169.52 - 5000 = 5169.52

After three more years, that becomes
5159.52*(1.093807)^3 = \$ 6751.98

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