to offer scholarships to children of employees, a company invests $11,000 at the end of every three months…
to offer scholarships to children of employees, a company invests $11,000 at the end of every three months in an annuity that pays 11% compounded quarterly. a. how much will the company have in scholarship funds at the end of ten years? b. find the interest. click the icon to view some finance formulas. a. the company will have $ in scholarship funds. (do not round until the final answer. then round to the nearest dollar as needed.)
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 annuity payment, $r$ is the interest rate per period, and $n$ is the number of periods.
Step2: Determine the values of $A$, $r$, and $n$
The annuity payment $A=$11000$. The annual interest rate $i = 11%=0.11$. Since it is compounded quarterly, the interest rate per period $r=\frac{0.11}{4}=0.0275$. The number of years is $t = 10$ years. Since there are 4 quarters in a year, the number of periods $n=10\times4 = 40$.
Step3: Calculate the future - value of the annuity
Substitute $A = 11000$, $r=0.0275$, and $n = 40$ into the formula: [ \begin{align*} F&=11000\times\frac{(1 + 0.0275)^{40}-1}{0.0275}\ &=11000\times\frac{(1.0275)^{40}-1}{0.0275} \end{align*} ] First, calculate $(1.0275)^{40}\approx2.995992$. Then $(1.0275)^{40}-1\approx1.995992$. $\frac{(1.0275)^{40}-1}{0.0275}=\frac{1.995992}{0.0275}\approx72.603345$. And $F = 11000\times72.603345\approx798636.795$.
Answer:
$798637$