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cyrus deposits a fixed quarterly amount into an annuity account for his child’s college fund. he wishes to accumulate a future value of $70,000 in 12 years. Assuming an APR of 3.3% compounded quarterly, how much of the $70,000 will cyrus ultimately deposit in the account, and how much is interest earned? round your answer to the nearest cent, if necessary. amount cyrus will deposit: $interest earned: $

Sagot :

Use the compound interest formula:

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

Cyrus is starting with $70,000, so P = 70000.

The interest rate is 3.3%, so r = 0.033.

Cyrus is compounded quarterly, this is compounding 4 times per year, so n = 4.

Cyrus wants to know the value of the account in 12 years, this is t = 12.

Then, Substitute using given values in the formula:

[tex]\begin{gathered} A=70000(1+\frac{0.033}{4})^{4\cdot10} \\ A=70000(1+\frac{0.033}{4})^{40} \\ A=97236.04 \end{gathered}[/tex]

This is ultimately deposited in the account.

For the interest, we have:

[tex]97236.04-70000=27236.04[/tex]

Answer:

amount cyrus will deposit: $ 97236.04

interest earned: $ 27236.04

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