Question

Consider the two savings plans below. Compare the balances in each plan after 7 years. Which person deposited more money in the​ plan? Which of the two investment strategies is​ better? Yolanda deposits ​$300 per month in an account with an APR of 6​%, while Zach deposits ​$3600 at the end of each year in an account with an APR of 6​%

Answer 1

Answer:

Zach´s strategy is better

Explanation:

To find the final capital, we use the compound interest formula:

Final Capital (FC)= Initial Capital (IC)*[(1+interest(i))]^(number of periods(n))

Yolanda:

She knows the APR (annual percentage rate) but she deposits each month, so we need to convert this rate in a montly rate. To do so, we use this formula:

Monthly rate= ((1+annual rate)^(1/# perdiods))-1

Montly rate= (1+6%)^(1/12)= 1,00486-1= 0,00486= 0,48%

Then, we apply the compound interest formula (84 periods because theare 84 months in 7 years):

FC= $300*(1+0,48%)^(84)= $451,09

Zach

We only need to apply the compound interest formula because he deposits each year and the rate is annual ( in this case the number of periods is ni year).

FC= $3600*(1+6%)^(7)=$4510,81