You are considering an investment in a 40-year security.The security will pay R25 a year at the end of each of the first three years.The security will then pay R30 a year at the end of each of the next 20 years.The simple interest rate is assumed to be 8 percent, and the current price (present value) of the security is R360.39.Given this information, what is the equal annual payment to be received from Year 24 through Year 40 (i.e., for 17 years)?

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the formula for the present value of an annuity:
PV = PMT⋅(1−(1+r)−n)/r
where PV is the present value, PMT is the equal annual payment, r is the interest rate, and n is the number of years.

We know that the present value of the security is R360.39 and the interest rate is 8%, so we can solve for the equal annual payment for the first 23 years using the first three payments of R25, followed by 20 payments of R30:
360.39 = 25⋅(1−(1+0.08)−3)/0.08 + 30⋅(1−(1+0.08)−20)/0.08 + PMT⋅(1−(1+0.08)−17)/0.08
Solving for PMT, we get PMT = R40.

Therefore, the equal annual payment to be received from Year 24 through Year 40 is also R40, making the best choice C.

You Are Considering an Investment in a 40-Year Security