Question

Yani has $12,000 for investment purposes. His bank has offered the following three choices:

Choice 1. A special savings certificate that will pay $120 each month for 5 years and a lump sum payment at the end of 5 years of $13,000
Choice 2. Buy a share of a racehorse for $12,000 that will be worth $27,000 in 5 years
Choice 3. Put the money in a savings account that will have an interest rate of 12% per year compounded monthly

Use an annual worth analysis to make a recommendation to Yani.

What is the annual worth of each choice?

Choice 1, Certificate=
Choice 2, Racehorse=

Choice 3, Savings Account=

(Boos solution is wrong)

Answer 1

The bank is offering an interest of 12% compounded monthly. Calculating the effective interest rate.

Effective rate of interest = 12.68% per annum.

First calculating the present worth of all the alternatives.

Choice 1.

Now converting it to Annual worth

AW1 = 550.45(A/P,12.68%,5) = $ 155.29

Choice 2. The annual worth of income can be calculated as follows

AW2 = -12,000(A/P,12.68%,5) +27,000(A/F,12.68%,5)

= - 12,000 × 0.28211 + 27,000 × 0.15529

= $ 807.45

Choice 3. The future value of the investment will be

FW3 = 12,000(F/P,12.68%,5) = 12,000 × 1.8166 = $ 21,800.36

Now convert it to annual worth

AW = -12,000(A/P,12.68%,5) +21,800.36(A/F,12.68%,5)

= $ 0

Choice 2 is best.

Last option annual worth is zero because I have used the same interest rate bank offers.