You will receive a $100 annual perpetuity, the first payment to be received now, at Year 0, a $300 annual perpetuity payable starting at the end of Year 5, and a $200 semiannual (2 payments per year) perpetuity payable starting midw through Year 10.If you require an effective annual interest rate of 14.49 percent, what is the present value of all thr perpetuities together at Year 0? (Hint: The semiannual annuity can be thought of as two annual annuities.)
A)$2,091.86
B)$2,785.14
C)$4,213.51
D)Infinite; the present value of any perpetuity is infinite.
E)Cannot determine the value since some payments are annually and some semiannually.

Question

Quizplus · Accepted Answer

The present value of each perpetuity is calculated separately and then summed. The $100 perpetuity starts now, the $300 perpetuity starts at Year 5, and the $200 semiannual perpetuity starts mid-Year 10. The semiannual perpetuity is treated as two annual perpetuities. The effective annual interest rate is used to discount each perpetuity to Year 0.

You Will Receive a $100 Annual Perpetuity, the First Payment