# 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 1.2%, compounded monthly, to meet her goal?

This type of a savings account is known as a sinking fund. The monthly payment M required to produce the desired amount of money (Future Value, or FV), when the period interest rate is R, is determined by the formula

`M = FV*R/((1+R)^N - 1)` , where N is the number of periods.

In this problem, the future value is FV = \$10,000 minus the amount of money Mary would like to save. The interest is compounded monthly, and the annual interest rate is 1.2%, so the period (monthly) interest rate R is

`(1.2%)/12 = 0.1% = 0.001` .

The number of periods (months) in 5 years is N = 12(5) = 60.

Plugging these values in the formula above, we get

`M=\$10,000*0.001/((1+0.001)^60 - 1) = \$161.80` , rounded to the nearest cent.

The monthly payment Mary would have to make is \$161.80. If she will deposit money once a week, she should deposit the amount of

`(\$161.80)/4 = \$40.45` .

Mary should deposit \$40.45 each week in the given savings account in order to save \$10,000 at the end of 5 years.

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