Final answer:
The present value of $8,000 annual payments from a perpetuity starting 6 years from today, discounted at a 3% annual return, is approximately $229,985.32.
Step-by-step explanation:
The student's question requires a calculation of the present value of a perpetuity, given that the Bank Trust will pay $8,000 per year indefinitely, starting 6 years from today, with an interest rate of 3% annually. To find the present value of these payments today, you must use the formula for the present value of a perpetuity and adjust it for the fact that payments start in the future, not immediately.
To calculate the present value of the perpetuity starting in 6 years time, we first find the present value at the time the payments begin. The present value of a perpetuity formula is:
PV = P / r
where PV is the present value, P is the yearly payment, and r is the annual interest rate. For the given numbers, it would be:
PV = $8,000 / 0.03
PV = $266,666.67 (This is the value 6 years from today)
To find the present value today, we must discount this amount back 5 more years (since the first payment is 6 years away).
PV today = PV / (1 + r)^n
PV today = $266,666.67 / (1 + 0.03)^5
PV today = $266,666.67 / 1.159274074
PV today = $229,985.32 (approximately)
The value of these payments today is approximately $229,985.32 when discounted at an annual return of 3%.