Final answer:
To find the interest rate of return for a purchased stream of annuity payments, the present value of annuity formula is used, and the interest rate is determined by solving for the rate that equates the given present value with the value of the annuity payments. The process involves testing the given options and selecting the rate that approximates the present value of $22,950.
Step-by-step explanation:
To determine the interest rate of return earned when paying $22,950 for a stream of $6,000 payments lasting 10 years, we need to use the present value of an annuity calculation. This calculation will allow us to find the interest rate that equates the present value of the annuity payments to the amount paid for the stream of payments.
First, we list out the given variables:
- Present Value (PV) = $22,950
- Periodic Payment (PMT) = $6,000
- Number of Periods (n) = 10 years
Then, we use the present value of annuity formula:
PV = PMT * [(1 - (1 + r)^-n) / r]
Where r is the rate of return (interest rate) and must be solved for. Without a financial calculator or spreadsheet software, this would typically require trial and error or financial tables to approximate the answer.
By plugging our option rates into the formula or using a financial calculator, we seek the rate that closely results in a present value of $22,950. Option A (5%), B (6%), C (7%), and D (8%) must all be tested.
The correct answer would be the rate that brings the present value closest to $22,950 without going over, assuming annuity payments at the end of each period. Since the precise calculation can be complex and not easily done without a financial calculator or software, this method will lead us to an approximate answer, unless one of the provided rates exactly matches the present value.