What is the present value of a growing perpetuity, where the first payment of $140 occurs one year from now, after which payments will grow at the constant rate of 3% p.a., and where the interest rate is 10% p.a.?

Question 1Answer

a.
$2000

b.
$2013

c.
$1948

d.
$2031

The present value of a growing perpetuity is calculated using the following formula:

\[
PV = \frac{C}{r - g}
\]

Where:
- $PV$ is the present value,
- $C$ is the first payment,
- $r$ is the interest rate (or discount rate),
- $g$ is the growth rate.

### Given values:
- $C = 140$,
- $r = 10\% = 0.10$,
- $g = 3\% = 0.03$.

Now, plug these values into the formula:

\[
PV = \frac{140}{0.10 - 0.03} = \frac{140}{0.07}
\]

\[
PV = 2000
\]

### The correct answer is:
**a. $2000**

Would you like further details or clarifications?

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Here are 5 related questions to consider:
1. How would the present value change if the interest rate increases to 12%?
2. What happens to the present value if the growth rate is reduced to 2%?
3. How is a growing perpetuity different from a regular perpetuity?
4. Can the present value of a growing perpetuity become infinite? Why or why not?
5. How does changing the timing of the first payment affect the formula?

**Tip:** The present value of a growing perpetuity is sensitive to the difference between the interest rate and the growth rate. If $r \leq g$, the formula doesn't work!

What is the present value of a growing perpetuity, where the first payment of $140 occurs one year from now, after which payments will grow at the constant rate of 3% p.a., and where the interest rate is 10% p.a.?

Learn how to calculate the present value of a growing perpetuity, starting with a $140 payment, with payments growing at 3% annually and a discount rate of 10%. This problem uses the present value of a growing perpetuity formula and explores financial concepts important for university-level finance and business students.

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