Question

The current price of a stock is $400 per share and it pays no dividends. Assuming a constant interest rate of 8% per year compounded quarterly, what is the stock's theoretical forward price for delivery in 9 months? Please submit your answer rounded to two decimal places so for example, if your answer is 567.1234 then you should submit an answer of 567.12

Answer 1

Answer: The stock's theoretical forward price for delivery in 9 months will be $424.48 .

Explanation:

Calculation by compound interest is a bit different from simple interest.

In this question, we have , the rate of interest is annual and the interest is compounded quarterly (i.e., 3 months or, 4 times in a year) then the number of years (n) is 4 times (i.e. made 4n) and the rate of annual interest (r) is one-fourth (i.e., made $\frac{r}{4}$).  

In such cases we use the following formula for compound interest when the interest is calculated quarterly.

If the principal = P,  rate of interest per unit time = $\frac{r}{4}$ % , number of units of time = 4n , the amount = A,

A = P ( 1 + $(\frac{\frac{r}{4} }{100})$  )$.^{4n}$

Using the above formula in the given question,

P = 400 , n = $\frac{3}{4}$ , r = $\frac{8}{100}$

A = 400 ( 1 + $\frac{0.08}{4}$ )$.^{3}$

A = $424.48

The stock's theoretical forward price for delivery in 9 months will be $424.48 .