Question

How much must be deposited today into the following account in order to have $50,000 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 5.9%

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$50000\\ P=\textit{original amount deposited}\\ r=rate\to 5.9\%\to (5.9)/(100)\dotfill &0.059\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &7 \end{cases}`

`50000=P\left(1+(0.059)/(4)\right)^(4\cdot 7) \implies 50000=P(1.01475)^(28) \\\\\\ \cfrac{50000}{(1.01475)^(28)}=P\implies 33183.05\approx P`