dr. j. wants to buy a dell computer that will cost $3,000 three years from today. he would like to set aside…

dr. j. wants to buy a dell computer that will cost $3,000 three years from today. he would like to set aside an equal amount at the end of each year in order to accumulate the amount needed. he can earn an 8% annual return. how much should he set aside at the end of each year? (round your answer to the nearest dollar). a $794 b $924 c $926 d $1,000 e none of the choices

dr. j. wants to buy a dell computer that will cost $3,000 three years from today. he would like to set aside an equal amount at the end of each year in order to accumulate the amount needed. he can earn an 8% annual return. how much should he set aside at the end of each year? (round your answer to the nearest dollar). a $794 b $924 c $926 d $1,000 e none of the choices

Answer

Explanation:

Step1: Use the future - value of an ordinary annuity formula

The formula for the future - value of an ordinary annuity is $FVA = A\times\frac{(1 + r)^{n}-1}{r}$, where $FVA$ is the future value of the annuity, $A$ is the annual payment, $r$ is the interest rate per period, and $n$ is the number of periods. We know that $FVA=$3000$, $r = 0.08$, and $n = 3$. We need to solve for $A$.

Step2: Rearrange the formula to solve for $A$

From $FVA = A\times\frac{(1 + r)^{n}-1}{r}$, we can get $A=\frac{FVA\times r}{(1 + r)^{n}-1}$.

Step3: Substitute the values

Substitute $FVA = 3000$, $r=0.08$, and $n = 3$ into the formula. First, calculate $(1 + 0.08)^{3}=1.08^{3}=1.259712$. Then $(1 + 0.08)^{3}-1=1.259712 - 1=0.259712$. And $FVA\times r=3000\times0.08 = 240$. So $A=\frac{240}{0.259712}\approx924$.

Answer:

B. $924$