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?
b. How much interest would the investment earn for the period?
c. What would be the effective rate of the investment?
2. Assume that you decide to invest the $4,000 in the high-interest savings account.
a. What future value would you expect to receive at the end of 6 months?
b. How much interest would the investment earn for the period?
c. What would be the effective rate of the investment?
To calculate the future value, interest earned, and effective rate of the investment, we can use the compound interest formula:
Future Value = Principal * (1 + (Interest Rate / Compounding Frequency))^(Compounding Frequency * Time)
where:
- Principal is the initial investment amount
- Interest Rate is the annual interest rate
- Compounding Frequency is the number of times the interest is compounded per year
- Time is the investment term in years
1. Investment in Certificate of Deposit:
a. To calculate the future value of the CD at the end of the investment term, we need to plug in the values into the formula:
Principal = $4,000
Interest Rate = 6% per year (0.06)
Compounding Frequency = 12 (monthly compounding)
Time = 6 months (0.5 years)
Future Value of the CD = $4,000 * (1 + (0.06 / 12))^(12 * 0.5)
b. To calculate the interest earned, we subtract the initial investment amount (Principal) from the future value:
Interest Earned = Future Value of the CD - Principal
c. To find the effective rate of the investment, we need to calculate the annual interest rate that would give us the same future value if compounded annually. To do this, we can rearrange the compound interest formula:
Effective Rate = (1 + (Interest Rate / Compounding Frequency))^(Compounding Frequency) - 1
2. Investment in High-Interest Savings Account:
a. To calculate the future value of the savings account at the end of 6 months:
Principal = $4,000
Interest Rate = 3% per year (0.03)
Compounding Frequency = 365 (daily compounding)
Time = 6 months (0.5 years)
Future Value of the savings account = $4,000 * (1 + (0.03 / 365))^(365 * 0.5)
b. To calculate the interest earned, we subtract the initial investment amount (Principal) from the future value:
Interest Earned = Future Value of the savings account - Principal
c. To find the effective rate of the investment, we can use the same formula as in the CD calculation.
By plugging in the given values into the respective formulas, you can calculate the answers to the questions.