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. $332,3667.36
c. $338,082.42
d. $281.059.48
Can you please walk me through this problem.
d 281,059.48
To find the present value of Andrew's estimated payments, we need to calculate the present value of an annuity.
The formula to calculate the present value of an annuity is:
PV = PMT × [(1 - (1 + r)^-n) / r]
Where:
PV is the present value
PMT is the annual payment amount
r is the interest rate per period
n is the total number of periods
Let's calculate the present value using the given information:
Annual payment (PMT) = $26,000
Interest rate (r) = 6% = 0.06
Number of periods (n) = 90 - 65 = 25 (from age 65 to 90)
First, we need to calculate (1 + r)^-n. Let's substitute the values:
(1 + 0.06)^-25 = 0.422407
Now, let's calculate the present value:
PV = $26,000 × [(1 - 0.422407) / 0.06]
PV = $26,000 × 7.956783
PV = $206,579.418
Therefore, the present value of Andrew's payments is approximately $206,579.418.
Because none of the answer choices match exactly, it seems there might be a rounding error. Let's round the answer to the nearest cent:
PV ≈ $206,579.42
Therefore, the answer is not one of the provided options, and there might be a mistake in the question or answer choices.