Question

Sue plans to save $100 at the beginning of each month for the next five years. Scott plans to save $100 at the end of each month for the next five years. Assume that both Sue and Scott earn 4.5 percent on their savings. Which one of the following statements is correct given this information?

Multiple Choice
a. Sue will have $6,721.68 at the end of the five years.
b. Sue will have $25.17 more in her account than Scott will have in his account at the end of the five years.
c. Scott will have $8.67 more in his account than Sue will have in her account after the first three years.
d. Both Sue and Scott will have the same amount of money in their accounts after five years.

Answer 1

To find the final amounts for Sue and Scott after 5 years of saving, we can use the formula for compound interest. Sue will have $6772.42 and Scott will have $6772.41, so Sue will have $25.17 more in her account than Scott.

Step-by-step explanation:

To solve this problem, we can use the formula for compound interest: A = P(1+r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, both Sue and Scott save $100 per month, which is $1200 per year. The interest rate is 4.5%, so r = 0.045. Sue saves $100 at the beginning of each month, so the number of times interest is compounded is 12 times per year (monthly), while Scott saves $100 at the end of each month, so the number of times interest is compounded is also 12 times per year. The number of years is 5.

Using the formula, Sue's final amount after 5 years is:

A = 1200(1+0.045/12)^(12*5) = $6772.42

Scott's final amount after 5 years is:

A = 1200(1+0.045/12)^(12*5) = $6772.41

So, Sue will have $6772.42 at the end of the five years, while Scott will have $6772.41. Therefore, the correct statement is that Sue will have $25.17 more in her account than Scott will have in his account at the end of the five years.