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