Question

Recall that the Sampsons would like to save a total of $1,000 per month. They notice that their local bank offers the certificate of deposit (CD) rates listed in the following table; they now need to determine if they should invest in CDs, and if so, which CDs will best suit their savings goals. The Sampsons are saving for a down payment on a new car that they will purchase for Sharon within a year. They hope to save money each month for their children’s college education, which begins twelve years from now.

Maturity	Annualized Interest Rate (%)
1 month	1.0
3 months	1.2
6 months	1.6
1 year	2.0
3 years	2.5
5 years	2.8
7 years	3.0
10 years	3.2

1. Advise the Sampsons on the maturity to select if they decide to invest their savings in a CD for a down payment on a car. Discuss the advantages and disadvantages of the maturity that you recommend the Sampsons use to save for the down payment on a car.

2.Advise the Sampsons on the maturity to select if they decide to invest their savings in CDs for their children’s education. Discuss the advantages and disadvantages of the maturity that you recommend the Sampsons use to save for their children’s education needs.

3.If you thought that interest rates were going to rise in the next few months, how might this affect the advice that you give the Sampsons about investing in CDs with short-term versus long-term maturities?

Answer 1

Part 1.

Since the investment is towards down payment for car one year, it is better to opt for the maturity within one year which gives highest rate. As per the given schedule, the bank offers 2% for one year and rates for shorter periods are lesser. Hence advised to invest in CD for one year.

Advantage of opting this term is that it gives the highest rate of return and matches the timing of requirement. Disadvantage is that in case the money is needed before completion of one year, they will have to suffer penalty for prepayment.

Part 2:

Since the investment horizon (for college education) s 12 years. Hence the best option from the given set is to invest initially for 10 years which yields the highest at 3.2% and then twice for one year each at 2%. This will result in the maturity value as follows:

[(+i₁)^n₁] * (1+i₂)^n₂   Where i1= interest rate of initial deposit (3.2%), i2= interest rate of subsequent deposits (2%), n1= period of initial deposit (10 years) and n2= period of subsequent deposits (2 years)

Maturity value of $1 = [(1+3.2%)^10]*(1+2%)^2 = $ 1.425599

The option is to first deposit for 7 years at 3% and then for 5 years at 2.8%. In this case, maturity value of $ 1 will be as follows:

[(1+3%)^7]*(1+2.8%)^5 = $ 1.411972

Hence the first option, ie., initially for 10 years and then twice for one year each is advised.

Advantage of this plan is highest return for the investment horizon. Disadvantage is the likely penalty for prpayment in case the money is needed before completion of 10 years initially or after that, before completion of one each.

Part 3.

In case the interest rates were going to rise in the next few months, the advise will be opt shorter duration initially. This is to make use of the higher rates likely after a few months for the remaining period of investment horizon.