to save money for her sons college tuition, heather invests $1022 every year in an annuity that pays 6%…

to save money for her sons college tuition, heather invests $1022 every year in an annuity that pays 6% interest, compounded annually. payments will be made at the end of each year. find the total value of the annuity in 22 years. do not round any intermediate computations, and round your final answer to the nearest cent. if necessary, refer to the list of financial formulas.

to save money for her sons college tuition, heather invests $1022 every year in an annuity that pays 6% interest, compounded annually. payments will be made at the end of each year. find the total value of the annuity in 22 years. do not round any intermediate computations, and round your final answer to the nearest cent. if necessary, refer to the list of financial formulas.

Answer

Explanation:

Step1: Identify the formula for future - value of an ordinary annuity

The formula for the future - value of an ordinary annuity is $F = A\times\frac{(1 + r)^{n}-1}{r}$, where $A$ is the annual payment, $r$ is the interest rate per period, and $n$ is the number of periods.

Step2: Identify the values of $A$, $r$, and $n$

We are given that $A=$1022$, $r = 0.06$ (since 6%=0.06), and $n = 22$ years.

Step3: Substitute the values into the formula

$F=1022\times\frac{(1 + 0.06)^{22}-1}{0.06}$. First, calculate $(1 + 0.06)^{22}$. Using the exponent formula, $(1 + 0.06)^{22}=1.06^{22}\approx3.548065$. Then, $(1 + 0.06)^{22}-1\approx3.548065 - 1=2.548065$. $\frac{(1 + 0.06)^{22}-1}{0.06}=\frac{2.548065}{0.06}\approx42.46775$. Finally, $F = 1022\times42.46775\approx43302.04$.

Answer:

$$43302.04$