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Sagot :
Given:
Interest rate = 2.5% compounded quarterly
Final Amount = $20,000
Time = 15 years
Let's find the amount you should invest in the account.
Here, we are to find the principal amount.
Apply the formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where:
A is the final amount = $20,000
r is the rate = 2.5% = 0.025
compound frequency is n. Since it is compounded quarterly, n = 4
t is the time in years = 15 years.
Let's solve for P.
We have:
[tex]\begin{gathered} 20000=P(1+\frac{0.025}{4})^{4\times15} \\ \\ 20000=P(1+0.00625)^{60} \\ \\ 20000=P(1.00625)^{60} \end{gathered}[/tex]Solving further:
[tex]20000=P(1.45329)[/tex]Divide both sides by 1.45329:
[tex]\begin{gathered} \frac{20000}{1.45329}=\frac{P(1.45329)}{1.45329} \\ \\ 13761.87=P \\ \\ P=13761.87 \end{gathered}[/tex]Therefore, the amount that should be invested is $13,761.87
ANSWER:
$13,761.87
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