Question

Using a discount rate of 9.6% APR, compounded monthly, calculate the present value of a monthly perpetuity con‐ sisting of $5200 payments if: (a) the first payment is made today (2 pts.), (b) the first payment is made one month from now (2 pts.), and (c) the first payment is made 42 months from now (2 pts.). [For part c, you want to be sure to master the two paragraphs in Lesson 2 about delayed perpetuities.]

Answer 1

(a) the first payment is made today, present value is $655,200

(b) The first payment is made one month from today: $650,000

(c) The first payment is made 42 months from today: $468,847.43

Step-by-step explanation:

We have the discount rate is: APR/12 = 9.6%/12 = 0.8% per month;

one discounting period is equal to 1 months.

(a) The first payment is made today, present value is the sum of today payment + present value of the perpetuity made in one-month time and last forever:

5,200 + 5,200/0.8% = $655,200.

(b) The first payment is made one month from today, present value is the present value of the perpetuity made in one-month time and last forever: 5,200/8% = $650,000

(c)The first payment is made 42 months from today, present value is the present value of the perpetuity in month 41st discounting 41 period, which is calculated as:

(5,200/0.8%) / (1+0008)^41 = $468,847.43.