Question

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%

Answer 1

`F=p(1+(r)/(n))^(nt)`

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

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

Therefore the present value deposited today = $29,985.40