Answered

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How much would you need to deposit in an account now in order to have $3000 in the account in 15 years? Assume theaccount earns 5% interest compounded quarterly.

Sagot :

Okay, here we have this:

According with the provided information, we are going to replace in the following formula:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Replacing we obtain:

[tex]\begin{gathered} 3000=P(1+\frac{0.05}{4})^{4\cdot15} \\ \end{gathered}[/tex]

Now, let's solve for P, that is the principal investment:

[tex]\begin{gathered} P\mleft(1+\frac{0.05}{4}\mright)^{4\cdot\: 15}=3000 \\ P\frac{4.05^{60}}{4^{60}}=3000 \\ P=3000\cdot\frac{4^{60}}{4.05^{60}} \\ P\approx1,423.70 \end{gathered}[/tex]

Finally we obtain that the deposit wold be aproximately of $1,423.70.

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