Question

You have a chance to buy an annuity that pays $3,750 at the end of each year for 6 years. You could earn 6.5% on your money in other investments with equal risk. What is the most you should pay for the annuity? * a) $1,107.97 b) $1,120 c) $1,108.98 d) $1,106.97

Answer 1

Correct answer is $18153.80

Here, the cash inflows will be same every year, so it is an annuity. We need to calculate the present value of annuity here. We will use the following formula:

PVA = P * (1 - (1 + r)-n / r)

where, PVA = Present value of annuity, P is the periodical amount = $3750, r is the rate of interest = 6.5% and n is the time period = 6

Now, putting these values in the above formula, we get,

PVA = $3750 * (1 - (1 + 6.5%)-6 / 6.5%)

PVA = $3750 * (1 - ( 1+ 0.065)-6 / 0.065)

PVA = $3750 * (1 - ( 1.065)-6 / 0.065)

PVA = $3750 * (1 - 0.68533411879) / 0.065)

PVA = $3750 * (0.31466588121 / 0.065)

PVA = $3750 * 4.8410135570

PVA = $18153.80

So, the value of annuity today is $18153.80