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How much must be doposited today into the following account in order to have $45,000 in 6 years for a down payment on a house? Assume no additional deposits are made.An account with annual compounding and an APR of 7%

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Solution

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

where:

F=future value = 45000

P=present value

r=rate (as a decimal) = 7%=0.07

n=number of compounding periods per year = 1

t=number of years = 6

[tex]\begin{gathered} F=p(1+\frac{r}{n})^{nt} \\ 45000=p(1+\frac{0.07}{1})^{1(6)} \\ 45000=P(1+0.07)^6 \end{gathered}[/tex][tex]\begin{gathered} 45000=P(1.07)^6 \\ 45000=P(1.50073) \\ P=\frac{45000}{1.50073} \\ P=29985.4 \end{gathered}[/tex]

Therefore the present value deposited today = $29,985.40

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