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Suppose that Sarah, age 30, opens a bank account paying 1.85% annual interest compounded monthly. She plans to deposit $250 each month in the account. Assuming the interest is the same for the next 35 years, how much will Sarah's account be worth when she retires at age 65? Compare her accumulation to her total investment both in absolute and relative terms. 

Guest Nov 25, 2017

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This is the formula you would use to calculate the FV of her deposits:

FV=P{[1 + R]^N - 1/ R}

FV=250 x {[1 + 0.0185/12]^(35*12) - 1 / (0.0185/12)}

FV=250 x {[1.0015416667]^420 - 1 / (0.0015416667)}

FV=250 x {[1.9098054874 - 1] / (0.001541667)}

FV=250 x {[0.9098054874 / 0.001541667]}

FV=250 x               590.144099920........... 

FV=$    147,536.02 - The amount of Sarah's retirement fund at 65. 

Her total deposits for the same period would be:

$250 x 420 months =$105,000. So, the difference would be:

$147,536.02  -  $105,000 =$42,536.02 interest earned @ 1.85% over 35 years.

Its Net Present Value =$77,251.86.

$147,536.02  -  $77,251.86 =$70,284.16 - Difference between FV and NPV.

Guest Nov 25, 2017
edited by Guest  Nov 25, 2017
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1+0 Answers

 #1
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0
Best Answer

This is the formula you would use to calculate the FV of her deposits:

FV=P{[1 + R]^N - 1/ R}

FV=250 x {[1 + 0.0185/12]^(35*12) - 1 / (0.0185/12)}

FV=250 x {[1.0015416667]^420 - 1 / (0.0015416667)}

FV=250 x {[1.9098054874 - 1] / (0.001541667)}

FV=250 x {[0.9098054874 / 0.001541667]}

FV=250 x               590.144099920........... 

FV=$    147,536.02 - The amount of Sarah's retirement fund at 65. 

Her total deposits for the same period would be:

$250 x 420 months =$105,000. So, the difference would be:

$147,536.02  -  $105,000 =$42,536.02 interest earned @ 1.85% over 35 years.

Its Net Present Value =$77,251.86.

$147,536.02  -  $77,251.86 =$70,284.16 - Difference between FV and NPV.

Guest Nov 25, 2017
edited by Guest  Nov 25, 2017

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