To solve for the required rate of return using a finance calculator, we can use the formula for the present value of a perpetuity. The formula for the present value of a perpetuity is:
\[ PV = \frac{C}{r} \]
where:
- \( PV \) = present value
- \( C \) = cash flow per period (annual payment)
- \( r \) = required rate of return (as a decimal)
Given:
- \( PV = 41,485.00 \)
- \( C = 4,830.00 \)
We need to solve for \( r \). Rearranging the formula gives us:
\[ r = \frac{C}{PV} \]
Plugging in the given values:
\[ r = \frac{4,830.00}{41,485.00} \]
Now, calculating that:
\[ r = 0.1163 \]
To express \( r \) as a percentage, multiply by 100:
\[ r \times 100 = 11.63% \]
Therefore, the required rate of return must be approximately 11.63%.
Steps on a finance calculator:
- Enter the cash flow amount (C = 4830) into the calculator.
- Enter the present value (PV = -41485) - note that it should be negative since it is an outflow.
- Use the appropriate function (usually titled as "Yield" or "IRR") to compute for the required rate of return (r).
- If your calculator allows, ensure you specify it's an ordinary annuity since the first payment is received one year from today.
- The calculator should then return approximately 11.63%.
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