Final answer:
To calculate the APR of a perpetuity contract with a monthly payment of $2,263 and a selling price of $132,897, we multiply the monthly payment by 12 to get an annual payment, and use the present value formula for perpetuities. The calculated APR is approximately 20.44%.
Step-by-step explanation:
To calculate the Annual Percentage Rate (APR) on an investment vehicle like the perpetuity contract mentioned, we need to first convert the monthly payment into an annual payment and then use the present value formula for perpetuities.
The monthly payment is $2,263, so the annual payment would be $2,263 × 12 = $27,156. To find the APR, we use the perpetuity present value formula:
PV = PMT / r, where:
- PV is the present value ($132,897 in this case)
- PMT is the annual payment ($27,156)
- r is the annual interest rate (APR)
Rearranging the formula to solve for r gives us:
r = PMT / PV
Plugging in the numbers:
r = $27,156 / $132,897 ≈ 0.2044 or 20.44%
Thus, the APR on this investment vehicle is approximately 20.44%.