select the correct answer from each drop - down menu.\nelwood invested $5,000 in a money market account and…

select the correct answer from each drop - down menu.\nelwood invested $5,000 in a money market account and has been tracking its progress. he found that after 3 years, the account held $7,100 and after 8 years, the account held $10,350.\nuse this information to complete the statements.\nover the first 3 years, the value of the account increased at \nover the last 5 years. over the entire 8 years, the value of the account increased at an average rate of approximately $ annually.

select the correct answer from each drop - down menu.\nelwood invested $5,000 in a money market account and has been tracking its progress. he found that after 3 years, the account held $7,100 and after 8 years, the account held $10,350.\nuse this information to complete the statements.\nover the first 3 years, the value of the account increased at \nover the last 5 years. over the entire 8 years, the value of the account increased at an average rate of approximately $ annually.

Answer

Explanation:

Step1: Calculate average rate for first 3 - years

The initial investment is $P = 5000$, and the value after 3 years is $A_1=7100$. The increase in value is $\Delta A_1=7100 - 5000=2100$. The average - rate of increase per year for the first 3 years is $r_1=\frac{7100 - 5000}{3}=\frac{2100}{3}=700$.

Step2: Calculate average rate for last 5 - years

The value after 3 years is $A_1 = 7100$, and the value after 8 years is $A_2 = 10350$. The increase in value is $\Delta A_2=10350 - 7100 = 3250$. The average - rate of increase per year for the last 5 years is $r_2=\frac{10350 - 7100}{5}=\frac{3250}{5}=650$. Since $700>650$, the value of the account increased at a faster rate over the first 3 years.

Step3: Calculate average rate for 8 - year period

The initial investment is $P = 5000$, and the value after 8 years is $A = 10350$. The increase in value is $\Delta A=10350 - 5000 = 5350$. The average - rate of increase per year for the 8 - year period is $r=\frac{10350 - 5000}{8}=\frac{5350}{8}=668.75\approx669$.

Answer:

Over the first 3 years, the value of the account increased at a faster rate over the last 5 years. Over the entire 8 years, the value of the account increased at an average rate of approximately $$669$ annually.