# Math

posted by Stacy

I really need some help with this one.

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?

1. MathMate

Six-month certificate of deposit at 6% p.a. compounded monthly, equivalent to 6/12=0.5% per period (month).

Principal = 4000
Future value, FV = 4000*1.005^6 = 4121.51
Interest earned = FV-principal
Effective rate = (interest/principal)*12months/6 months

2. Stacy

Thanks MathMate. The second part of the question is about the high interest savings account that pays 3% compounded daily. How do you do it daily?

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. MathMate

I would rather stay with the 6%.
Daily interest sounds good, but not at half the interest rate of 3%. You basically follow the same procedure as in the 6% compounded monthly, but divide the interest rate by 365, and compound every day.

Here's how it works:

High interest at 3% p.a. compounded daily, equivalent to 3/365% per period (day). Six-months = 183 days, approx.

Principal = 4000
Future value, FV = 4000*(1+3/365)^183 = 4060.62
Interest earned = FV-principal
Effective rate = (interest/principal)*12months/6 months

Note that the effective rate is for six-months prorated to a year. It would be slightly higher if the money was deposited for a whole year.

Also, if the six-month certificate had been compounded daily, the future value would have added \$0.63 to the pot, even though daily interest sounds soooo good!

4. Stacy

Thanks sgain for the help, I really appreciate it.

5. MathMate

You're welcome!

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