Answer:
$2821.67.
Explanation:
The formula for calculating the amount, A in an account for an initial deposit, P compounded k times in a year for t years at a rate of r% is:
[tex]A=P(1+\frac{r}{k})^{kt}[/tex]In the given problem:
• The amount that will be in the account, A(t) = $4,000
,• Time, t=5 years
,• Rate, r = 7% = 0.07
,• k=12 (compounded monthly)
We want to find the value of P.
[tex]\begin{gathered} 4000=P(1+\frac{0.07}{12})^{12\times5} \\ \implies P=4000\div(1+\frac{0.07}{12})^{12\times5}=4000\div1.4176 \\ P=\$2821.67 \end{gathered}[/tex]You would need to deposit $2821.67.
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