Question

As an employee in the Lottery Commission, your job is to design a new prize. Your idea is to create two grand prize choices: (1) receiving $50,000 at the end of each year beginning in one year for 20 consecutive years, or (2) receiving $500,000 today followed by a one-time payment at the end of 20 years. Using an interest rate of 6%, which of the following comes closest to the amount prize (2) needs to pay at the end of year 20 in order that both prizes to have the same present value?

	a.	$ 326,649
	b.	$ 235,712
	c.	$ 393,342
	d.	$ 440,463
	e.	$ 114,932

Please have the detail explanation thank you.

Answer 1

Option B is correct

Step 1. Present Value of Prize 1

First of all we will calculate the present value of Prize 1

Present Value = 50,000 * Present Value Annuity Factor 6%, 20 Years

Present Value = 50,000 * 11.4699 = 573496.06

Step 2

In Prize 2 we will recieve 500000 today, ie we have 73496.06 (573496.06-500000) recievable

This amount of 73496.06 which is recievable will be compounded at the rate of 6% for 20 years

Future Value of 73496.06 at the end of 20 Years = 73496*(1.06)^20

Future Value = 235711.82