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math formula?

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Mary would like to save $10 000 at the end of 5 years for a future down payment on a car. How much should she deposit at the end of each week in a savings account that pays 12%/a, compounded monthly, to meet her goal?

d. Determine the weekly deposit without technology.

Can someone provide me with the formula please?

  • math formula? - ,

    That is called a sinking fund

    Since it is compounded monthly do it all monthly and divide the deposit by 4 to get the weekly figure.

    S =D [ (1+r)^n -1 ] /r
    S is what we need at the end, in this case 10,000
    D is the monthly deposit (remember divide it by four for weekly)
    n is the number of compounding periods, in this case 5*12 = 60
    r is the interest rate (decimal) at each compounding period, in this case .12/12 = .01
    so
    10,000 = D[ 1.01)^60 -1 ] / .01
    10,000 = D (0.817)/.01 = D (81.7)
    D = 122.44
    D/4 = $30.61 per week

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