which of the following accounts will yield the greatest amount of interest on an initial deposit of…

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula is $A = P(1 + r)^n$, where $P$ is the principal amount, $r$ is the annual interest rate (as a decimal), $n$ is the number of years, and the interest $I=A - P=P((1 + r)^n-1)$. Here, $P = 1000$.

Step2: Calculate interest for option A

For option A, $r = 0.07$ and $n = 4$. Then $I_A=1000((1 + 0.07)^4-1)=1000(1.07^4 - 1)$. $1.07^4=1.07\times1.07\times1.07\times1.07 = 1.31079601$, so $I_A=1000(1.31079601 - 1)=310.79601$.

Step3: Calculate interest for option B

For option B, $r = 0.05$ and $n = 3$. Then $I_B=1000((1 + 0.05)^3-1)=1000(1.05^3 - 1)$. $1.05^3=1.05\times1.05\times1.05 = 1.157625$, so $I_B=1000(1.157625 - 1)=157.625$.

Step4: Calculate interest for option C

For option C, $r = 0.04$ and $n = 6$. Then $I_C=1000((1 + 0.04)^6-1)=1000(1.04^6 - 1)$. $1.04^6=1.04\times1.04\times1.04\times1.04\times1.04\times1.04\approx1.26531902$, so $I_C=1000(1.26531902 - 1)=265.31902$.

Step5: Calculate interest for option D

For option D, $r = 0.06$ and $n = 5$. Then $I_D=1000((1 + 0.06)^5-1)=1000(1.06^5 - 1)$. $1.06^5=1.06\times1.06\times1.06\times1.06\times1.06\approx1.33822558$, so $I_D=1000(1.33822558 - 1)=338.22558$.

Answer:

D. Account that pays 6% interest compounded annually for 5 years.