At the beginning of each year Apple declares a dividend of 7 to be paid semi-annually. An economist forecasts an increase of 9% per year. At the beginning of the year Bob buys some shares at $X per share and optimistically predicts a 22% yield convertible semi-annually.

Calculate X.

• $54.68
• $87.40
• $113.62
• $65.77
• $103.94

Hardiek, Aaron (June 2010). "Study Questions for Actuarial Exam 2/FM". digitalcommons.calpoly.edu. Retrieved November 20, 2023.

Solution: E

The first thing to notice that isn’t entirely apparent is that this is a perpetuity. We nest need to find k, which in this case will be the first yearly payment. This will be:

[[math]] K = 7s_{\overline{2}|.11} = 14.77 [[/math]]

Next we need to find the yearly interest rate:

[[math]] i = (1 + .22/2)^2 – 1 = .2321 r = .09 [[/math]]

Since i > r

[[math]] \textrm{PV} = k/(i + r) = 14.77/(.2321 - .09) = 103.94. [[/math]]

Hardiek, Aaron (June 2010). "Study Questions for Actuarial Exam 2/FM". digitalcommons.calpoly.edu. Retrieved November 20, 2023.