To solve the problem, we're dealing with a perpetuity. The value of a perpetuity can be calculated using the formula:
\[ PV = \frac{PMT}{r} \]
Where:
- \( PV \) = Present Value (Amount you pay today)
- \( PMT \) = Payment received each period (perpetuity payment)
- \( r \) = Required rate of return (as a decimal)
Given:
- \( PV = 47,698 \)
- \( PMT = 4,887 \)
We want to solve for \( r \): \[ r = \frac{PMT}{PV} \]
Now substituting the given values:
\[ r = \frac{4,887}{47,698} \]
Calculating \( r \):
\[ r = 0.102646 \text{ or } 10.26% \]
Now, if you wish to use a finance calculator and input values directly, typically for solving for the rate of return, you'd use the following inputs:
- \( N \) (Number of periods): Use a very large number (many calculators might allow you to skip this for perpetuity problems)
- \( PMT \) (Payment): \( 4,887 \)
- \( i/y \) (Interest rate): Will be solved
- \( FV \) (Future Value): \( 0 \) (since it’s a perpetuity, we do not consider the future value)
- \( PV \) (Present Value): \( -47,698 \) (it’s entered as a negative because it’s cash outflow when you pay for the investment)
In summary:
- \( N \): can often be left blank for perpetuity or a large number
- \( PMT \): 4,887
- \( i/y \): Solve for this
- \( FV \): 0
- \( PV \): -47,698
After inputting these values, use the “compute” feature for \( i/y \) to find the required rate of return. It should reflect approximately \( 10.26% \).