Envision that you have served as business manager of Media World for over 2 years. You have noticed that for the last 12 months the business has regularly had cash assets of $20,000 or more at the end of each month. You have found a 6-month certificate of deposit that pays 6% compounded monthly. To obtain this rate of interest, you must invest a minimum of $2,000. You have also found a high interest savings account that pays 3% compounded daily. Based on the cash position of the business at this time, assume that you decide to invest $4,000.
1. Assume that you will invest the full amount in a certificate of deposit.
a. What would be the future value of the CD at the end of the investment term? (14 points)
b. How much interest would the investment earn for the period? (14 points)
c. What would be the effective rate of the investment?(14 points)
To calculate the future value of the certificate of deposit (CD) at the end of the investment term, you will need to use the formula for compound interest:
Future Value = Principal * (1 + (Rate / n))^(n * t)
Where:
- Principal is the initial investment ($4,000)
- Rate is the annual interest rate (6% or 0.06)
- n is the number of times interest is compounded per year (12, since it's compounded monthly)
- t is the number of years the money is invested (6 months / 12 = 0.5 years)
a. Plugging in the values:
Future Value = $4,000 * (1 + (0.06 / 12))^(12 * 0.5)
Future Value = $4,000 * (1 + (0.005))^6
Future Value = $4,000 * (1.005)^6
Future Value ≈ $4,249.46
The future value of the CD at the end of the investment term would be approximately $4,249.46.
b. To calculate the interest earned for the period, subtract the initial investment:
Interest = Future Value - Principal
Interest = $4,249.46 - $4,000
Interest ≈ $249.46
The investment would earn approximately $249.46 in interest.
c. The effective rate of the investment can be calculated using the following formula:
Effective Rate = ((1 + (Rate / n))^(n * t) - 1) * 100
Plugging in the values:
Effective Rate = ((1 + (0.06 / 12))^(12 * 0.5) - 1) * 100
Effective Rate = ((1 + (0.005))^6 - 1) * 100
Effective Rate ≈ 6.14%
The effective rate of the investment would be approximately 6.14%.
To calculate the future value of the certificate of deposit (CD), we can use the formula for compound interest:
Future Value = Principal * (1 + interest rate/number of times compounded)^(number of times compounded * number of years)
In this case, the principal is $4,000, the interest rate is 6% (0.06), and the CD is compounded monthly. Let's calculate the future value:
Future Value = $4,000 * (1 + 0.06/12)^(12 * 0.5)
= $4,000 * (1.005)^(6)
≈ $4,242.55
Therefore, the future value of the CD at the end of the investment term would be approximately $4,242.55.
To calculate the interest earned for the period, we can subtract the initial investment from the future value:
Interest earned = Future Value - Principal
= $4,242.55 - $4,000
= $242.55
Therefore, the CD investment would earn approximately $242.55 in interest for the period.
To calculate the effective rate of the investment, we can use the formula for the effective annual interest rate:
Effective Rate = (1 + interest rate/number of times compounded)^(number of times compounded) - 1
In this case, the interest rate is 6% (0.06), and the CD is compounded monthly. Let's calculate the effective rate:
Effective Rate = (1 + 0.06/12)^12 - 1
= (1.005)^12 - 1
≈ 0.0617 or 6.17%
Therefore, the effective rate of the investment would be approximately 6.17%.