An investor was afraid that he would become like King Lear in his retirement and beg hospitality from his children, so he purchased grain "tithes," or shares in farm output, for 640 pounds. The tithes paid him 70 pounds per year for 31 years. What interest rate did the he receive on this investment?

Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.

To determine the interest rate received on the investment, we can approach this as a problem of calculating the internal rate of return (IRR) for an annuity. The investor receives \( 70 \) pounds per year for 31 years, and the initial investment was \( 640 \) pounds.

The formula to calculate the present value of an annuity is given by:

\[
PV = \frac{P}{r} \times \left( 1 - \frac{1}{(1 + r)^n} \right)
\]

Where:
- \( PV \) is the present value (initial investment, 640 pounds),
- \( P \) is the annual payment (70 pounds),
- \( r \) is the interest rate (which we are solving for),
- \( n \) is the number of years (31 years).

We need to solve for \( r \). Since the equation cannot be solved algebraically for \( r \), we can use numerical methods such as trial and error or more efficient iterative methods to find the interest rate that satisfies the equation.

Let's solve this numerically.The interest rate that the investor received on the investment is approximately **10.43%**.

Would you like more details on the calculation or have any other questions?

Here are five related questions you might find helpful:
1. How does changing the number of years affect the interest rate calculation?
2. What is the difference between nominal and effective interest rates?
3. How can the internal rate of return (IRR) be used in other investment decisions?
4. What is the formula for calculating the present value of a perpetuity instead of an annuity?
5. How would taxes affect the net interest rate in this scenario?

**Tip:** Always compare different types of investments using their effective interest rates, as they take compounding into account!

An investor was afraid that he would become like King Lear in his retirement and beg hospitality from his children, so he purchased grain 'tithes,' or shares in farm output, for 640 pounds. The tithes paid him 70 pounds per year for 31 years. What interest rate did he receive on this investment? Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.

Discover how to calculate the internal rate of return (IRR) for an investment in farm tithes, where an investor receives 70 pounds per year for 31 years after an initial investment of 640 pounds. The solution involves financial mathematics, including the present value of annuities and iterative methods. Suitable for college-level finance students.

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