A bank account earned 2% annual interest, compounded daily, for as long as the balance was under $1,000, starting when the account was opened. Once the balance reached $1,000, the account earned 2.5% annual interest, compounded daily until the account was closed. No deposits or withdrawals were made. Was the total amount of interest earned at the 2% rate greater than the total amount earned at the 2.5% rate?

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8 July, 16:00

A bank account earned 2% annual interest, compounded daily, for as long as the balance was under $1,000, starting when the account was opened. Once the balance reached $1,000, the account earned 2.5% annual interest, compounded daily until the account was closed. No deposits or withdrawals were made. Was the total amount of interest earned at the 2% rate greater than the total amount earned at the 2.5% rate?

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Patricky · Answer 1

Yes, it was larger, since the total interest earned at the 2% was $39.43

Explanation:

If the account was open for only 3 years, and it earned $25 in interest at the 2.5% rate:

Interest earned = principal x (1 + r) ⁿ - principal

25 = 1,000 x (1 + 0.025/365) ⁿ - 1,000

1,025 = 1,000 x (1 + 0.025/365) ⁿ

(1 + 0.025/365) ⁿ = 1,025 / 1,000 = 1.025

1.00006849ⁿ = 1.025

n = 361 days

this means that it took exactly 734 days for the account to reach $1,000, and the most an account with a $1,000 balance can earn with an interest rate of 2% is $20.20. That means that the account's initial balance must have been $960.57.

If the initial balance was $960.57, during the 734 days it earned $39.43, which is larger than $25.