Final answer:
The question involves two steps: first, calculating the future value of retirement savings with annual contributions and a fixed return, and second, determining the annual retirement income using a present value interest factor of an annuity over a set period.
Step-by-step explanation:
The question involves calculating the future value of retirement savings using the annuity formula and then determining the annual retirement income using the concept of present value of an annuity. First, we calculate the future value of the savings after 25 years based on the initial savings of $15,000 and annual contributions of $2,900 with a 7% annual return. Then we use the future value as a lump sum to determine the annual retirement income over 20 years at the same 7% return rate, considering the provided present value interest factor of an annuity (PVIFA) of 10.59401.
To calculate the future value of the retirement savings (FV), we use the formula:
FV = PV * (1 + r)^n + PMT * [((1 + r)^n - 1) / r]
where:
- PV = present value or initial amount ($15,000)
- PMT = annual payment or contribution ($2,900)
- r = annual interest rate (7% or 0.07)
- n = number of periods (25 years)
Once we compute the future value, we calculate the annual retirement income by dividing the future value by the PVIFA for 20 years at a 7% discount rate. This is essentially the reverse of calculating the present value of an annuity.