Help! I have had several solutions and cannot come up with an answer. Thank you!
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?
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?
3. Media World- Write a recommendation to the partners justifying a short-term investment of business funds at this time, recommending one of these investments. Include your analysis from question 1 and 2 in your recommendation.
To answer the questions regarding the investments in the certificate of deposit (CD) and high-interest savings account, we need to make use of compound interest formulas and calculations. Let's break down the steps for each question.
1. Assume that you will invest the full amount of $4,000 in a certificate of deposit.
a. To find the future value of the CD at the end of the investment term, we can use the formula for compound interest:
FV = P(1 + r/n)^(nt)
Where:
FV = future value
P = principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case, the interest rate is 6% per year, compounded monthly. So, r = 0.06, n = 12, and t = 6/12 = 0.5 (since it's a 6-month investment).
Plugging these values into the formula, we get:
FV = $4,000(1 + 0.06/12)^(12*0.5)
FV = $4,000(1 + 0.005)^(6)
FV ≈ $4,126.89
Therefore, the future value of the CD at the end of the investment term would be approximately $4,126.89.
b. To calculate the amount of interest earned by the investment, we need to subtract the initial investment from the future value:
Interest = FV - P
Interest = $4,126.89 - $4,000
Interest ≈ $126.89
The investment would earn approximately $126.89 in interest for the period.
c. The effective rate of the investment can be calculated using the formula:
Effective Rate = (1 + r/n)^(n) - 1
Plugging in the values, we get:
Effective Rate = (1 + 0.06/12)^(12) - 1
Effective Rate ≈ 0.0616 or 6.16%
Therefore, the effective rate of the investment is approximately 6.16%.
Now, let's move on to the high-interest savings account.
2. Assume that you decide to invest the $4,000 in the high-interest savings account.
a. To find the future value in the high-interest savings account, we can use the same compound interest formula:
FV = P(1 + r/n)^(nt)
The interest rate is 3% per year, compounded daily. So, r = 0.03, n = 365, and t = 6/12 = 0.5.
Plugging in the values, we get:
FV = $4,000(1 + 0.03/365)^(365*0.5)
FV ≈ $4,019.52
Therefore, the expected future value at the end of 6 months would be approximately $4,019.52.
b. The interest earned by the investment is calculated by subtracting the initial investment from the future value:
Interest = FV - P
Interest = $4,019.52 - $4,000
Interest ≈ $19.52
The investment would earn approximately $19.52 in interest for the period.
c. The effective rate of the investment can be calculated using the formula mentioned earlier:
Effective Rate = (1 + r/n)^(n) - 1
Plugging in the values, we get:
Effective Rate = (1 + 0.03/365)^(365) - 1
Effective Rate ≈ 0.0303 or 3.03%
Therefore, the effective rate of the investment is approximately 3.03%.
Now, for question 3, we need to write a recommendation to the partners justifying a short-term investment of business funds:
Based on the analysis, I would recommend investing the business funds in the high-interest savings account for the following reasons:
1. The future value of the high-interest savings account is slightly higher than the certificate of deposit, providing a better return on investment.
2. The interest earned in the high-interest savings account is also greater than that of the certificate of deposit for the same period.
3. Despite the lower interest rate, the effective rate of the high-interest savings account is still higher than the certificate of deposit, thus maximizing the return on investment for the 6-month period.
Considering these factors, investing the business funds in the high-interest savings account would be a more advantageous choice in terms of potential returns.