An investment account opens with $4500. Compound interest accrues at 8% per annum, credited quarterly.The least number of quarters needed for the value of this account to exceed $6000 is:

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BlackTom AI · Accepted Answer

We start with the given principal of 4500 and a nominal annual rate of 8% compounded quarterly. The quarterly rate is 0.08/4 = 0.02, so after n quarters the account value is 4500*(1.02)^n.

We want the smallest n such that 4500*(1.02)^n > 6000. Dividing both sides by 4500 gives (1.02)^n > 6000/4500 = 4/3 ≈ 1.3333.

Taking natural logarithms, n*ln(1.02) > ln(4/3).

Calculate the logs: ln(1.02) ≈ 0.019802 and ln(4/3) ≈ 0.287682. So n > 0.287682 / 0.019802 ≈ 14.52.

Since n must be an integer number of quarters, the smallest integer greater than 14.52 is 15. To sanity-check, compute approximate balances:
- After 14 quarters: 4500*(1.02)^14 ≈ 4500*1.319 ≈ 5935, which is below 6000.
- After 15 quarters: 4500*(1.02)^15 ≈ 4500*1.345 ≈ 6053, which exceeds 6000.

Therefore, it takes 15 quarters for the value to exceed 6000.

MUF0141 Fund. Mathematics Unit 1 - Semester 1, 2025 7.5 Simple & Compound Interest Quiz (Formative)

An investment account opens with $4500. Compound interest accrues at 8% per annum, credited quarterly.The least number of quarters needed for the value of this account to exceed $6000 is:

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