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tanja wants to establish an account that will supplement her retirement income beginning 10 years from now. find the lump sum she must deposit today so that $200,000 will be available at time of retirement, if the interest rate is 6%, compounded quarterly. (round to the nearest cent as needed)

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Solution

For this case we can use the following formula:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

And for this case

n= 4 compounded quarterly

t= 10 years

A= 200000

P=?

r=0.06

And we can solve for P and we got:

[tex]P=\frac{200000}{(1+\frac{0.06}{4})^{4\cdot10}}=110252.5[/tex]

So then the final answer would be:

110252.5