Posted by **Chris** on Wednesday, February 19, 2014 at 3:02pm.

Betty Sue sets up a retirement account. For the first 35 years, she deposits

$500 at the end of each month into an account with an annual interest rate of 3.6%, compounded monthly. Then, she stops making monthly payments and transfers the money into a different account with an annual interest rate of 4%, compounded quarterly for a period of 10 years. How much money has she saved for retirement at the end of her 45 years if saving?

- Finite Math and Applied Calculus -
**Damon**, Wednesday, February 19, 2014 at 3:14pm
first 35 years

35 * 12 = 420 months = n

r = .036/12 = .003 monthly interest rate

p= present value of sinking fund

N = deposit each period of 1 month = 500

p = N [ (1+r)^n - 1 ] /r

p = 500 [ (1.003)^420 - 1 ] / .003

p = 419,796.33 after 35 years

now the final 10 years

quarterly for 10 years = 40 periods

interest rate = .04/4 = .01

1.01^40 = 1.48886

times 419 etc = 625,019.54

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