Question

How much must be deposited today into the following account in order to have $ 40000 in 7 years for a down payment on a​ house? Assume no additional deposits are made.

An account with quarterly compounding and an APR of 6.7%
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Part 1 $?? should be deposited today.
​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 40000\\ P=\textit{original amount deposited}\\ r=rate\to 6.7\%\to (6.7)/(100)\dotfill &0.067\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &7 \end{cases}`

`40000 = P\left(1+(0.067)/(4)\right)^(4\cdot 7) \implies 40000=P(1.01675)^(28) \\\\\\ \cfrac{40000}{(1.01675)^(28)}=P\implies 25122.50\approx P`