Question

Calculate, to the nearest cent, the Present Value of an investment that will be worth $1,000 at the stated interest rate after the stated amount of time.

3 years, at 1.3% per year, compounded weekly (52 times per year).

PV=?

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 1000\\ P=\textit{original amount deposited}\\ r=rate\to 1.3\%\to (1.3)/(100)\dotfill &0.013\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, thus fifty two} \end{array}\dotfill &52\\ t=years\dotfill &3 \end{cases}`

`1000 = P\left(1+(0.013)/(52)\right)^(52\cdot 3) \implies 1000=P(1.00025)^(156) \\\\\\ \cfrac{1000}{(1.00025)^(156)}=P\implies 961.76\approx P`