to save money for a sabbatical to earn a masters degree, henry deposits $2000 at the end of each year in an…

to save money for a sabbatical to earn a masters degree, henry deposits $2000 at the end of each year in an annuity that pays 6.7% compounded annually. use the formula for the value of an annuity, shown to the right. a. how much will he have saved at the end of four years? b. find the interest. a. how much money will be in the annuity four years later? $ (do not round until the final answer. then round to the nearest dollar as needed.)

to save money for a sabbatical to earn a masters degree, henry deposits $2000 at the end of each year in an annuity that pays 6.7% compounded annually. use the formula for the value of an annuity, shown to the right. a. how much will he have saved at the end of four years? b. find the interest. a. how much money will be in the annuity four years later? $ (do not round until the final answer. then round to the nearest dollar as needed.)

Answer

Explanation:

Step1: Identify the values of variables

$P = 2000$, $r=0.067$, $n = 1$, $t = 4$.

Step2: Substitute values into the annuity - formula

$A=\frac{2000\left[\left(1+\frac{0.067}{1}\right)^{1\times4}-1\right]}{\frac{0.067}{1}}$. First, calculate the value inside the brackets: $\left(1 + 0.067\right)^{4}=1.067^{4}\approx1.29503$. Then $1.067^{4}-1\approx1.29503 - 1=0.29503$. Next, $2000\times0.29503 = 590.06$. Finally, $A=\frac{590.06}{0.067}\approx8807$.

Step3: Calculate the total amount of deposits

The total amount of deposits in 4 years is $2000\times4 = 8000$.

Step4: Calculate the interest

Interest $=A - 2000\times4$. Substitute $A\approx8807$ into the formula, Interest $\approx8807-8000 = 807$.

Answer:

a. $8807$ b. $807$