Answer:
After 3 years, Jong will have approximately $539.85 in his account, while DeAndre will have approximately $538.45 in his account. Therefore, Jong will have more money when he closes his account.
Explanation:
To determine who has more money when they close their accounts, we can calculate the final amounts for both Jong and DeAndre.
First, let's calculate the amount Jong will have after 3 years with quarterly compounding:
Formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (initial deposit).
r is the annual interest rate (in decimal form).
n is the number of times that interest is compounded per year.
t is the number of years.
For Jong:
P = $500
r = 2.5% or 0.025 (in decimal form)
n = 4 (compounded quarterly)
t = 3 years
A = 500(1 + 0.025/4)^(4*3)
A = 500(1 + 0.00625)^(12)
A = 500(1.00625)^12
A ≈ 500(1.07971)
A ≈ $539.85
Now, let's calculate the amount DeAndre will have after 3 years with annual interest calculation:
For DeAndre:
P = $500
r = 2.5% or 0.025 (in decimal form)
n = 1 (calculated annually)
t = 3 years
A = 500(1 + 0.025/1)^(1*3)
A = 500(1 + 0.025)^3
A = 500(1.025)^3
A ≈ 500(1.07689)
A ≈ $538.45