Final answer:
The monthly return on the perpetual annuity contract that pays $3,000 monthly is 0.92%, the APR is 11.04%, and the effective annual return is 11.71%.
Step-by-step explanation:
The live perpetual annuity contract in question pays out $3,000 monthly and is priced at $326,000. To calculate the monthly return, we can use the return on investment (ROI) formula:
Monthly Return = Monthly Payment / Price
Thus, the monthly return is:
Monthly Return = $3,000 / $326,000 = 0.0092 or 0.92%
To find the Annual Percentage Rate (APR), we multiply the monthly return by 12:
Annual Percentage Rate (APR) = 0.0092 * 12 = 0.1104 or 11.04%
The effective annual return (EAR) takes into account the compounding within the year. Since the annuity pays monthly, we would use the formula for the effective annual rate:
EAR = (1 + monthly return)^12 - 1
Assuming the monthly return is compounded, the EAR is:
EAR = (1 + 0.0092)^12 - 1 = 0.1171 or 11.71%
The calculations demonstrate that investing in the annuity will yield a monthly return of 0.92%, an APR of 11.04%, and an effective annual return of 11.71%.