# Nancy deposits \$300 into her savings account at the end of every 3 months for 2 years. If the account pays 3.5%/a, compounded quarterly, how much money will Nancy have in  the account at the end of 2 years?

Nancy has \$2474.8 in her account at the end of 2 years. Nancy deposits \$300 into her savings account at the end of every 3 months for 2 years. The account pays 3.5% per annum, compounded quarterly, and the amount Nancy has after 2 years has to be determined.

If an amount P is invested at the rate of interest r, the amount after t years is equal to P*(1+r)^t. As compounding is done quarterly in the problem, the applicable rate of interest is 3.5/4 = 0.875% and the number of terms for t years is 4*t.

The amount in Nancy's account after 2 years is equal to

`300*(1+0.00875)^8+300*(1+0.00875)^7+300*(1+0.00875)^6+...300*(1+0.00875)^1`

= `300*(1.00875^8+1.00875^7+...1.00875)`

= `300*(1-1.00875^8)/(1-1.00875)`

= `300*8.249`

= 2474.8

Nancy has \$2474.8 in her account at the end of 2 years.

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