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# Ryan deposits 75,000 quarterly in a bank with a offers 6% interest compundly semi annually. How much is the future after 4 years?

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Ryan deposits 75,000 quarterly in a bank with a offers 6% interest compundly semi annually. How much is the future after 4 years?

Sep 21, 2017

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This is the formula you would use to calculate the FV:
FV=P{[1 + R]^N - 1/ R}

But before you do that, you must match the compounding period of the interest rate, which is semi-annual, to the periodic deposits, which are compounded quarterly. We know that 6% is compounded semi-annually, which means every 6 months you would multiply by 1.03. Now, we can turn this into quarterly compound as follows: 1.03^1/2 =1.0148891565 -1 =0.0148891565. This is the quarterly interest rate that you would use in the above formula.

FV = 75,000 x {[1 + 0.0148891565]^(4*4) - 1 / 0.0148891565}
FV = 75,000 x {[       0.2667700813876161] / 0.0148891565}
FV = 75,000 x            17.91707148673..........
FV =\$1,343,780.36 - This is what Ryan will have saved in 4 years.

Sep 21, 2017