Andrew decides to wait until age 65 to begin receiving social security benefits. Find the present value of his estimated $26,000 per year in payment assuming 6%per year and payment until his 90th birthday.
A. $265,263.20
B. $322,3667.36
C. $338,082.42
D. $281,059.48
(Please walk me through it)
To find the present value of Andrew's estimated $26,000 per year payment, we need to calculate the value of future cash flows in today's dollars. We can use the formula for the present value of an annuity.
The formula for the present value of an annuity is:
PV = P * (1 - (1 + r)^(-n)) / r
Where:
- PV is the present value
- P is the annual payment amount ($26,000)
- r is the interest rate per period (6% or 0.06 as a decimal)
- n is the number of periods (years until his 90th birthday, which is 90 - 65 = 25 years)
Now let's calculate the present value using these values:
PV = $26,000 * (1 - (1 + 0.06)^(-25)) / 0.06
Calculating the result:
PV = $26,000 * (1 - (1.06)^(-25)) / 0.06
PV ≈ $265,263.20
Therefore, the present value of Andrew's estimated payments is approximately $265,263.20.
So, the correct answer is option A) $265,263.20.