Question

You have won the State Lottery that calls for you to receive $50,000 every six months for 20 years. The State uses a discount rate of 5.7 percent. If you wish to receive a lump sum amount of money today instead of the monthly payment, how much will you receive today?

Group of answer choices

$1,175,456.84

$1,372,917.25

$1,184,283.00

$1,399,512.75

$2,000,000.00

Answer 1

Option (c) is correct

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

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

where, PVA = Present value of annuity, P is the periodical amount = $50000, r is the rate of interest =5.7% compounded semi annually, so semi annual rate = 5.7% / 2 = 2.85% and n is the time period = 20 * 2 = 40 semi annual years.

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

PVA = $50000 * (1 - (1 + 2.85%)^-40 / 2.85%)

PVA = $50000 * (1 - ( 1+ 0.0285)^-40 / 0.0285)

PVA = $50000 * (1 - ( 1.0285)^-40 / 0.0285)

PVA = $50000 * (1 - 0.32495869259) / 0.0285)

PVA = $50000 * (0.6750413074 / 0.0285)

PVA = $50000 * 23.6856599089

PVA = $1184283

So, lump sum payment amount is $1184283.