Question

In: Advanced Math

A lottery offers the chance to win a prize of receiving payments forever starting with $200...

A lottery offers the chance to win a prize of receiving payments forever starting with $200 for the first payment followed by each consecutive payment increasing by $250 until the payment size reaches $700. If you receive a payment every quarter, with the first in one quarter and interest is earned at j4 = 5%, what amount must the lottery have in the account today to fund the prize?

Solutions

Expert Solution

Firstly, following are the payments, without interest added, that need to be made by the lottery:

Payment 1: $200

Payment 2: $200+$250 = $450

Payment 3: $450+$250 = $700

This payment of $700 needs to be made "forever". Hence, these payments have to be made till perpetuity. A perpetuity is a constant stream of identical cash flows with no end. The formula for calculating the present value of this perpetuity is as follows:

Where D = Cash Flow per period = $700

and interest rate = 5% p.a compounded quarterly

So, the quarterly interest rate is 5/4 = 1.25 % per quarter

Hence r = 1.25%

Taking this into account, the Present Value of the perpetuity is:

or

So, the total perpetuity that needs to be paid is $56000. However, there are two more payments that need to be made i.e. payment 1 and payment 2

Payment 1 = $200
The interest rate of 1.25% needs to be added to payment 2.

So,

Payment 2 = 450 + 5.625

Payment 2 = 455.625

Therefore, Total amount the lottery should have in the account to fund the prize is Present Value of Perpetuity + Payment 1 + Payment 2

So, Total amount = 56000 + 200 + 455.625

Total amount in the lottery account = $56,655.625


Related Solutions

A town offers a lottery. To win the grand prize of $1,000,000, your ticket needs to...
A town offers a lottery. To win the grand prize of $1,000,000, your ticket needs to consist of the winning seven numbers chosen from the set {1, 2, …, 55}. To win the lesser prize of $10,000, your ticket needs to have exactly five of the seven. a) What is the probability of winning the grand prize? b) What is the probability of winning the lesser prize? c) If a lottery ticket costs $1, what is the expected value of...
1. You have just won a Colorado Lottery prize that will pay annual payments $7,573 forever....
1. You have just won a Colorado Lottery prize that will pay annual payments $7,573 forever. You would rather have a lump sum today rather than the future payments. If you wanted o discount those payments by 11.0%, the value of that prize in todays dollars would be $__.__. 2. Suppose that you were to receive $105 at the end of year one, $230 at the end of year 2, and $352 at the end of year three. If the...
Suppose that you win the Lottery. The stated prize is $402 million. If you agree to...
Suppose that you win the Lottery. The stated prize is $402 million. If you agree to take the payout over 30 years in the form of an annuity due, then each payment equals the stated prize divided by 30. The first payment will be made to you immediately, and the remaining 29 future payments will be paid out annually (beginning one year from today). Alternatively, you can take the lump sum payout. This payout is calculated as the present value...
Harley's Daycare will run a promotional raffle that offers a chance to win either a lifetime...
Harley's Daycare will run a promotional raffle that offers a chance to win either a lifetime discount on merchandises (which results in a $1,000 savings) or a 5-year limited discount on any party-goods (which results in a $100 savings). Winning a lifetime discount has a 1-in-500 chance. Winning a 5-year limited discount has a 1-in-50 chance. Is this promotion worth it if the tickets cost $15? The promotion is not worth it. ONLY if you cannot answer F1, for partial...
What is the value of receiving $4,000 per month forever, the first cash flow starting in...
What is the value of receiving $4,000 per month forever, the first cash flow starting in one month, if the discount rate is a 3% monthly compounded APR? What if the discount rate is an annually compounded 3%?
The millionaire lottery winner won the $ 175,000,000 jackpot and has the option of receiving payments...
The millionaire lottery winner won the $ 175,000,000 jackpot and has the option of receiving payments of $ 7,000,000 annually for 25 years beginning in year 1 or taking $ 109,355,000 today. At what interest rate? Are the two options equivalent?
While in Mexico, you buy a lottery ticket and win. The award is 5 annual payments...
While in Mexico, you buy a lottery ticket and win. The award is 5 annual payments of MXN 1,000,000 with the first payment made today. The APR interest rate for 4 years of future MXN cash flows is 6% and for USD cash flows is 2%. The exchange rate today is MXN19.6/USD. What is the value today of your winnings in terms of USD? Show the result taking the present value (PV) in both currencies (hint: determine expected exchange rates...
On January 1, you win $56,250,000 in the state lottery. The $56,250,000 prize will be paid in equal installments of $6,250,000 over nine years.
Present value of an annuityOn January 1, you win $56,250,000 in the state lottery. The $56,250,000 prize will be paid in equal installments of $6,250,000 over nine years. The payments will be made on December 31 of each year, beginning on December 31 of this year. The current interest rate is 6.5%.Determine the present value of your winnings. Round your answer to the nearest dollar.$ _________
An investment that currently sells for $200 makes payments every year forever, which grow annually at...
An investment that currently sells for $200 makes payments every year forever, which grow annually at a constant rate. If the annual return on this investment is 6% and next payment amount is $10, what is the constant rate at which the payments grow annually? At an annual interest rate of 7%, how many years does it take to triple your money? Today, you open a new savings account and deposit $5,000. No other deposits or withdrawals are made to...
n investment that currently sells for $200 makes payments every year forever, which grow annually at...
n investment that currently sells for $200 makes payments every year forever, which grow annually at a constant rate. If the annual return on this investment is 6% and next payment amount is $10, what is the constant rate at which the payments grow annually?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT