Question
George Jefferson established a trust fund that will provide $233,500 per year in scholarships. The trust fund earns an annual return of 4.2 percent. How much money did Mr. Jefferson contribute to the fund assuming that only income is distributed?
Answers
GPT-4o mini
To determine how much money Mr. Jefferson contributed to the trust fund, we can use the formula for the present value of an annuity. The annuity formula relates the annual payment, the interest rate, and the present value as follows:
\[
PV = \frac{PMT}{r}
\]
Where:
- \(PV\) is the present value (the initial amount contributed to the fund)
- \(PMT\) is the annual payment from the fund ($233,500)
- \(r\) is the annual interest rate (expressed as a decimal, so 4.2% = 0.042)
Plugging in the values:
\[
PV = \frac{233,500}{0.042}
\]
Now, performing the calculation:
\[
PV = \frac{233,500}{0.042} \approx 5,570,238.10
\]
Therefore, Mr. Jefferson contributed approximately **$5,570,238.10** to the fund.
\[
PV = \frac{PMT}{r}
\]
Where:
- \(PV\) is the present value (the initial amount contributed to the fund)
- \(PMT\) is the annual payment from the fund ($233,500)
- \(r\) is the annual interest rate (expressed as a decimal, so 4.2% = 0.042)
Plugging in the values:
\[
PV = \frac{233,500}{0.042}
\]
Now, performing the calculation:
\[
PV = \frac{233,500}{0.042} \approx 5,570,238.10
\]
Therefore, Mr. Jefferson contributed approximately **$5,570,238.10** to the fund.