Question

1. Using the appropriate interest factor table, answer each of the following questions (each case is independent of each other.)

1. Your company purchases a 5-year certificate of deposit which pays semi-annually and has a stated interest rate of 6.5%. The initial investment is $10,000. What is the future amount of your investment worth at the end of 5 years?
2. What amount must you put in the bank today if you will need $20,000 in 10 years for the cost of your child's college education? The bank will provide you with interest payments quarterly on your investment. The annual rate of interest you have been quoted is 9 percent.

Answer 1

Solution

(1)
Information provided as follows,
Interest payable semi-annually.
Therefore, Number of Compounding (m) = 2
Now, Initial Annual Interest Rate = 6.5%
So, Effective Rate of Return (r) = 6.5% / 2 = 3.25%
Again, Term of Investment = 2 Years
So, Effective Term (n) = 2 x 2 = 4

Now, if Initial Investment is $10,000, the future value of the Investment would be
= $10000 x (1 + 3.25%)⁴
= $10000 x 1.1365
= $11365

Therefore, if initial investment is $10000, future value would be $11365 under the given parameters.

(2)
Amount needed $20000 at the end of 10th year.
Annual Rate of Interest is 9%, and it is provided that the interest will be paid quarterly.
Therefore, Number of Compoundings = 4
Under given parameters,
Effective Rate of Interest (r) = 9% / 4 = 2.25%
and, Effective Term (n) = 10 x 4 = 40

Therefore, amount required today will be calculated as follows,
20000 = P x (1 + 2.25%)⁴⁰
Or, 20000 = P x 2.4352
Or, P = 20000 / 2.4352
Or, P = 8212.88

Therefore, $8212.88 should be invested today under the given the portfolio.