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how much must be deposited the beginning of each year in an account that pays 6% compounded annual so that the count will contain 22,000 at the end of four years

Respuesta :

We know that

• The interest rate is 6% (0.06).

,

• The compounding period is annual. (n = 1).

,

• The final amount is $22,000.

,

• The time is 4 years. (t = 4).

Let's use the compound interest formula

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

We have to replace the given values and solve for P

[tex]\begin{gathered} 22,000=P(1+\frac{0.06}{1})^{1\cdot4} \\ 22,000=(1.26)P \\ P\approx\frac{22,000}{1.26} \\ P\approx17,460.32 \end{gathered}[/tex]

Hence, there must be deposited $17,460.32, approximately.

To find the annual payment, first, we find the total earnings through the 4 years.

[tex]22,000-17,460.32=4,539.68[/tex]

Then, we divide by 4

[tex]\frac{4,539.68}{4}=1,134.92[/tex]

Hence, the annual payment is $1,134.92.

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