Question

Whitney deposited money into an account in which interest is compounded quarterly at a rate of

2. 9%. She made no other deposits or withdrawals and the total amount in her account after 12 years

was $10,891. 31.

How much did she deposit?

O

$7700

O

$8650

O

$9700

o $10,580

Next

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 10891.31\\ P=\textit{original amount deposited}\\ r=rate\to 2.9\%\to (2.9)/(100)\dotfill &0.029\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &12 \end{cases}`

`10891.31 = P\left(1+(0.029)/(4)\right)^(4\cdot 12) \implies 10891.31=P(1.00725)^(48) \\\\\\ \cfrac{10891.31}{1.00725^(48)}=P\implies 7700\approx P`