21
QuizMultiple Choice

N/A — Exam

Question 21 • Financial Math

Aahil and Zuri each invest $⁢4,000 Aahil puts his money into a simple interest account with an annual rate of 3.5% Zuri chooses an account that offers continuously compounded interest at a rate of 3% Determine how many years it will take for Zuri's continuously compounded interest account to surpass Aahil's simple interest account in terms of balance. After how many years will Zuri's balance exceed Aahil's? Simple Interest Formula: A=P⁢(1+r⁢t) Continuously Compounded Interest Formula: A=P⁢e^r⁢t The value of e , also known as Euler's number, is approximately 2.71828

Answer
A
Zuri's balance will exceed Aahil's balance after the 15th year.
B
Zuri's balance will exceed Aahil's balance between the 10th and the 12th year.
C
Zuri's balance will exceed Aahil's balance between the 12th and the 15th year.
D
Zuri's balance will exceed Aahil's balance before the 10th year.

Explanation

Both balances start at $4,000, so compare their growth factors: Aahil’s is 1 + 0.035t, and Zuri’s is e^(0.03t). After 10 years, Aahil’s factor is 1.35, while Zuri’s is e^0.3 ≈ 1.3499, so Zuri is still slightly behind. After 11 years, Aahil’s factor is 1.385 and Zuri’s is e^0.33 ≈ 1.391, so Zuri has pulled ahead between years 10 and 11. This matches choice B, between the 10th and 12th year.

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