Question

After receiving a reward for information leading to the arrest of a notorious criminal, you are considering investing it in an annuity that pays $5,000 at the end of each year for 20 years. You could earn 5% on your money in other investments with equal risk. What is the most you should pay for the annuity? Select one:
a. $50,753
b. $53,424
c. $56,236
d. $59,195
e. $62,311

Answer 1

Answer:

option (e) $62,311

Explanation:

Data provided in the question:

Annuity paid each year = $5,000

Annual payment = $5,000

Interest rate, r = 5%  = 0.05

Time period, n = 20 years

Now,

Present value of annuity = Annuity ×  $\frac{(1 - (\frac{1}{1 + r})^n)}{r}$

on substituting the respective values, we get

Present value of annuity = $5,000 ×  $\frac{(1 - (\frac{1}{1 + 0.05})^{20})}{0.05}$

or

Present value of annuity = $5,000 × 12.4622

or

Present value of annuity = $62,311

Hence,

The correct answer is option (e) $62,311