a staunch christian has willed an amount of $5500 to be paid annually forever to the bible house. At 91 day treasury bill rate of 12%, what is the present value of the donation if payment starts;
at the end of the year
at the beginning of the year
at the end of five years
To calculate the present value of the donation, we need to discount the future cash flows back to the present using the appropriate interest rate. In this case, the interest rate is given as the 91-day Treasury bill rate, which is 12%.
1. Payment at the end of the year:
To calculate the present value of a perpetuity (annuity paid forever) with end-of-year cash flows, we use the formula: Present Value = Cash Flow / Interest Rate.
In this case, the cash flow is $5,500 and the interest rate is 12%. So, the present value of the donation is $5,500 / 0.12 = $45,833.33.
2. Payment at the beginning of the year:
To calculate the present value of a perpetuity with beginning-of-year cash flows, we use the formula: Present Value = Cash Flow / (Interest Rate + 1).
In this case, the cash flow is still $5,500, and the interest rate is 12%. So, the present value of the donation is $5,500 / (0.12 + 1) = $50,000.
3. Payment at the end of five years:
To calculate the present value of an annuity with a finite period (five years), we use the formula: Present Value = Cash Flow * (1 - (1 + Interest Rate)^(-n)) / Interest Rate, where n is the number of periods.
In this case, the cash flow is $5,500, the interest rate is 12%, and the number of periods is 5. Plugging in these values, we get: Present Value = $5,500 * (1 - (1 + 0.12)^(-5)) / 0.12 = $21,256.46.
So, the present value of the donation depends on when the payment starts, with the values calculated as follows:
- Payment at the end of the year: $45,833.33
- Payment at the beginning of the year: $50,000
- Payment at the end of five years: $21,256.46.