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Math  /  Data & Statistics

Questionirement and other FV Question 6, 9.3.3 HW Score: 62.5%,562.5 \%, 5 of 8 points Part 2 of 4 Points: 0 of 1
Consider the two savings plans below. Compare the balances in each plan after 10 years. Which person deposited more money in the plan? Which of the two investment strategies is better? Yolanda deposits $100\$ 100 per month in an account with an APR of 6%6 \%, while Zach deposits $1200\$ 1200 at the end of each year in an account with an APR of 6%6 \%.
The balance in Yolanda's saving plan after 10 years was $16,387.93\$ 16,387.93. (Round the final answer to the nearest cent as needed. Round all intermediate values to seven decimal places as needed.) The balance in Zach's saving plan after 10 years was $\$ □\square (Round the final answer to the nearest cent as needed. Round all intermediate values to seven decimal places as needed.)

Studdy Solution

STEP 1

1. Yolanda deposits \$100 monthly with an APR of 6%.
2. Zach deposits \$1200 annually with an APR of 6%.
3. We need to calculate the future value (FV) of Zach's savings plan after 10 years.
4. Compounding is assumed to be annual for Zach's deposits.

STEP 2

1. Calculate the future value of Zach's savings plan.
2. Compare the total deposits made by Yolanda and Zach.
3. Determine which investment strategy is better based on the final balances.

STEP 3

Calculate the future value of Zach's savings plan using the formula for the future value of an annuity:
FV=P×(1+r)n−1r FV = P \times \frac{(1 + r)^n - 1}{r}
Where: - P=1200 P = 1200 (annual deposit) - r=0.06 r = 0.06 (annual interest rate) - n=10 n = 10 (number of years)

STEP 4

Substitute the values into the formula:
FV=1200×(1+0.06)10−10.06 FV = 1200 \times \frac{(1 + 0.06)^{10} - 1}{0.06}

STEP 5

Calculate the future value:
FV=1200×(1.06)10−10.06 FV = 1200 \times \frac{(1.06)^{10} - 1}{0.06}
FV=1200×1.790847−10.06 FV = 1200 \times \frac{1.790847 - 1}{0.06}
FV=1200×0.7908470.06 FV = 1200 \times \frac{0.790847}{0.06}
FV=1200×13.180783 FV = 1200 \times 13.180783
FV=15816.94 FV = 15816.94

STEP 6

Calculate the total deposits made by Yolanda:
Total Deposits by Yolanda=100×12×10=12000 \text{Total Deposits by Yolanda} = 100 \times 12 \times 10 = 12000
Calculate the total deposits made by Zach:
Total Deposits by Zach=1200×10=12000 \text{Total Deposits by Zach} = 1200 \times 10 = 12000

STEP 7

Compare the balances:
- Yolanda's balance after 10 years: \$16,387.93 - Zach's balance after 10 years: \$15,816.94
Determine which strategy is better:
- Yolanda's strategy results in a higher balance.
The balance in Zach's saving plan after 10 years is:
15,816.94 \boxed{15,816.94}
Yolanda deposited the same amount as Zach, but her strategy resulted in a higher balance, making it the better investment strategy.

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