Question

How much more would you need to deposit at the end of every month to accumulate $288,500 over 20 years if the interest rate earned is 5.0% compounded annually instead of 5.0% compounded monthly?

Answer 1

- Calculating the Annual Cash Flow using Interest rate compounded annually:-

$Future Value= C*\frac{[(1+r)^{n}-1]}{r}$

Where, C= Periodic Payments

r = Periodic Interest rate = 5%

n= no of periods = 20

Future Value = $288,500

$288,500= C*\frac{[(1+0.05)^{20}-1]}{0.05}$

$288,500= C*\frac{[2.65329770514-1]}{0.05}$​​​​​​

C = $8724.99

So, Annual Cash flow if Interset is compunded annually is $8724.99

- Calculating the Annual Cash Flow using Interest rate compounded Monthly:-

$Future Value= C*\frac{[(1+r)^{n}-1]}{r}$

Where, C= Periodic Payments

r = Periodic Interest rate = 5%/12 =0.41666%

n= no of periods = 20yrs*12 =240

Future Value = $288,500

$288,500= C*\frac{[(1+0.0041666)^{240}-1]}{0.0041666}$

$288,500= C*\frac{[2.71264028116-1]}{0.0041666}$

​​​​​​C = $701.89

So, Annual Cash flow if Interset is compunded Monthly is $701.89

So, the more you need to deposit every month = $8724.99 - $701.89

= $8023.10

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