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:

Question

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:

View Explanation

Log in for full answers

Similar Questions

Bob bought some land costing $14,990. Today that same land is valued at $55,000. How long has Bob owned this land if the price of land has been increasing at 6 percent per year?

If $5200 is placed in an account which pays 7% per annum, compounding annually, then the balance in the account after n years is calculated by:

Question at position 2 How long will it take for $600 to amount to $900 at an annual rate of 6% compounded quarterly?5 years, 3 months8 years, 1 month6 years, 9 1/2 months7 years, 2 months

Question at position 3 If $1,000 is invested for 2 years at 6% compounded quarterly, then the compound amount at the end of the period is$1593.84.$1126.49.$1120.00.$1141.23.$1123.60.

Your great aunt Matilda put some money in an account for you on the day you were born. This account pays 8% interest per year. On your 21st birthday the account balance was $5033.83. The amount of money that would be in the account if you left the money there until your 65th birthday is closest to:

Your great aunt Matilda put some money in an account for you on the day you were born. This account pays 8% interest per year. On your 21st birthday the account balance was $5033.83. The amount of money that your great aunt Matilda originally put in the account is closest to:

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler