Question

You have $15,000 to invest. A high-interest-rate CD offers to provide a 4% return, compounded daily, as long as the money is invested for at least 12 months.

Based on a 365-day year, how much would your CD be worth after 13 months? (Enter only the number--do not include the dollar sign; i.e. 15,325.48).
Hint: To calculate the number of days, multiply the number of months by 365 and divide by 12.
You have $15,000 to invest. A high-interest-rate CD offers to provide a 4% return, compounded daily, as long as the money is invested for at least 12 months.
Based on a 365-day year, how much would your CD be worth after 13 months? (Enter only the number--do not include the dollar sign; i.e. 15,325.48).
Hint: To calculate the number of days, multiply the number of months by 365 and divide by 12.

Answer 1

The $15,000 CD with a 4% return compounded daily is worth approximately $15,522.50 after 13 months.

Step-by-step explanation:

To calculate how much a $15,000 CD would be worth after 13 months with a 4% return compounded daily, we will use the formula for compound interest:

A = P(1 + r/n)(nt)

Where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money).
• r is the annual interest rate (decimal).
• n is the number of times that interest is compounded per year.
• t is the time the money is invested for, in years.

Here P is $15,000, r is 0.04 (4% expressed as a decimal), n is 365 (since the interest is compounded daily), and t is 13/12 (since we're calculating for 13 months).

First, we convert 13 months into days, which is (13 * 365) / 12 = 398.958 days approximately. Now we express t in years, which is 398.958 / 365 = approximately 1.093 years.

Now we can plug the values into the formula:

A = 15000(1 + 0.04/365)(365*1.093)

Calculating the above will give us the value of the CD after 13 months.

Using a calculator, we find that A ≈ $15,522.50.

Thus, the CD would be worth approximately $15,522.50 after 13 months.