Final answer:
The calculation involves finding the present value of a declining series of payments discounted at an annual effective interest rate of 6.5%. Each payment's present value is found using the formula PV = P/(1+i)^n, adjusting for the declining amount, and then summed to find the total present value.
Step-by-step explanation:
The subject question involves present value calculations and understanding how to calculate the present worth of a series of payments that are decreasing over time.
Given an annual effective interest rate of 6.5%, we need to find the present value of 30 payments starting at $1050 and decreasing by $15 each year.
To solve for X, the present value, we discount each of the payments back to the present using the formula for present value.
For each payment, the formula used is:
PV = P/(1+i)^n
Where:
PV = Present Value
P = Payment amount
i = Interest rate per period
n = Number of periods
We apply this formula to each payment, making sure to adjust the payment amount as it decreases by $15 each year. Once the present value of each individual payment is calculated, these values are summed to determine the total present value (X).