Finite Math and Applied Calculus

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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 di fferent 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 -

    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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