Question

Algebraically manipulating the formula FV = P(1 + p", how much money is needed as an initial deposit to reach a future value of $8,700, if the account isearning 7%, compounded quarterly, for 6 years to the nearest whole dollar)?$6,154.33$5,737.11$5,432.19$4,908,66None of these choices are correct.

Answer 1

The future value formula, given by

`FV=P(1+(r)/(n))^(nt)`

Can be used to obtain the Principal by substituting other values into the equation and solving for P

Step 1: List out the parameters given

FV =$8,700

r=7%=0.07

n=4 (since there are 4 quarters in a year)

t=6 (since it will be compounded 6 times a year)

Step 2: Substitute the values into the formula

`8700=P(1+(0.07)/(4))^{4\text{ x 6}}`
`8700=P(1+0.0175)^(24)`

`\begin{gathered} 8700=P(1.0175)^(24) \\ 8700=1.5164P \end{gathered}`

Solving for P

`\begin{gathered} 1.5164P=8700 \\ P=(8700)/(1.5164) \end{gathered}`

P=$5737.11

Option B is correct