Question

If the interest rate is 3% and a total of $4,370.91 will be paid to you at the end of 3 years, what is the present value of that sum? A$3,900.00 B3,947.00 C$3,977.40 D$4,000.00

Answer 1

`\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill&4370.91\\ P=\textit{original amount deposited}\dotfill \\ r=rate\to 3\%\to (3)/(100)\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases}`

`\bf 4370.91=P\left(1+(0.03)/(1)\right)^(1\cdot 3)\implies 4370.91=P(1.03)^3 \\\\\\ 4370.91=1.092727P\implies \cfrac{4370.91}{1.092727}=P\implies 4000.00183\approx P \\\\[-0.35em] \rule{34em}{0.25pt}`

which rounds up to... .yeap, you guessed it.