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Jong deposits $500 in an account that earns 2.5% interest compounded quarterly

and keeps the money in the account for 3 years. DeAndre deposits $500 in an account that earns
2.5% interest calculated 1 time, at the end of the same 3 years. Who has more money when he
closes his account?

1 Answer

5 votes

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

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