Question

You wish to have $200,000 at the end of twenty years. In the last five years, you withdraw $1,000 annually at a rate of 3.8% compounded quarterly. During the middle ten years, you contribute $500 monthly at a rate of 2.8% compounded semi-annually. Given this information, determine the initial deposit that has to be made at the start of the first five years at a rate of 4% compounded monthly.

Answer 1

The Initial deposit value is "62,812.42" .

Explanation:

The required amount in 15 years:

$\ \ \ \ \ \ \ \ \ \ \ \ \ =PV((1+\frac{3.8\%}{4})^{4}-1,5,1000,200000,0)*-1= \ 170,010.30$

The required amount in 5 years:

$=PV((1+\frac{2.8\%}{2})^{\frac{1}{6}}-1,10\times 12,-500,170010.3,0)*-1= \ 76,420.91$

So, the Initial deposit:

$=PV((1+4\%)^{\frac{1}{12}}-1,5 \times 12,0,-76420.91,0)= \ 62,812.42$

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