math formula?
posted by Aly on .
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?

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