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 $550 per month in an account with an APR of 6%, while Zach deposits $ 7000 at the end of each year in an account with an APR of 6.5
What is the balance in Yolanda's savings plan after 7 years?
To calculate the balance in Yolanda's savings plan after 7 years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit)
r = annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years the money is invested for
In this scenario:
P = $550 (monthly deposit)
r = 6% APR = 0.06 (annual interest rate in decimal form)
n = 12 (monthly contributions, or compounding frequency per year)
t = 7 (number of years)
Calculating the balance after 7 years for Yolanda's savings plan:
A = 550(1 + 0.06/12)^(12*7)
A = 550(1.005)^84
A ≈ $53,451.81
Therefore, the balance in Yolanda's savings plan after 7 years would be approximately $53,451.81.