Question

at the end of every 3 months, judy deposits $100 into an account that pays 6% compounded quarterly. after 4 years, she puts the accumulated amount into a certificate of deposit paying 7.5% compounded semiannually for 1 year. when this certificate matures, how much will judy have accumulated?

Answer 1

Quarterly seeds, six percent bloom, sprout $1731.54. Yearly sun warms savings, 7.5% sun-kissed, to harvest $1796.87.

To calculate how much Judy will have accumulated, we need to follow these steps:

Step 1: Calculate the interest earned each quarter for the first 4 years.

• Interest per quarter = $100 * (1 + 0.06 / 4)^4 - $100 ≈ $1.49
• Total interest for 4 years = $1.49 * 4 * 4 = $23.84

Step 2: Calculate the final balance after 4 years.

• Final balance after 4 years = $100 * (1 + 0.06 / 4)^16 + $23.84 ≈ $1731.54

Step 3: Calculate the interest earned each semester for the certificate of deposit.

• Interest per semester = $1731.54 * (1 + 0.075 / 2)^2 - $1731.54 ≈ $65.33

Step 4: Calculate the final balance after 1 year.

• Final balance after 1 year = $1731.54 + $65.33 ≈ $1796.87

Therefore, when the certificate matures, Judy will have accumulated approximately $1796.87.

Note: This is an approximation because we rounded the interest earned in each step. The actual amount may be slightly different due to compounding.