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Time Value of Money: Lottery Winnings, Home Shopping, Roth IRA

1. You won the lottery and will receive $50,000 per yr for 20 yrs. Assume 4% interest used to evaluate annuity and you receive pymt at the begining of the yr
a. what is the PV of the lottery b/ how much interest was earned on the PV to make $50,000 a year pymt.

2. You are shopping for a new home. You have a choice of financing. Either $200,000 at 5.75% for 30yrs or $200,000 at 5.5% for 15yrs. Calculate the mthly pymt for both 30 and 15 yrs mortg. Calculate the interest paid over the life of the loan for both mortgages. Choose the best mortgage for you and explain your answer.

3. Blushing invest $1000 into Roth IRA. She increase the investment annually by $1000 until she reaches the $5000 annual contribution limit. She will then invest $5000 per year at the beginning of each year for 30yrs. How much will blushing have in her IRA at the end on 34yrs if her IRA earns 8%.

Solution Preview

1. You won the lottery and will receive $50,000 per yr for 20 yrs. Assume 4% interest used to evaluate annuity and you receive payment at the beginning of the yr

a. what is the PV of the lottery
PVoa = PMT [(1 - (1 / (1 + i)^n)) / i]

Where:

PVoa = Present Value of an Ordinary Annuity
PMT = Amount of each payment
i = Discount Rate Per Period
n = Number of Periods

PVoa = PMT [(1 - (1 / (1 + i)^n)) / i]
= 50,000 [1-(1/1 + 0.04)^20))/0.04]
= 50,000 [(1- 1/2.1911)/0.04]
= 50,000 [(1-0.4564)/0.04]
= 50,000 [0.54361/0.04]
= 50,000 * 13.5903
= $ 679,515

b. how much interest was earned on the PV to make $50,000 a year payment.

FVoa = PMT [((1 + i)^n - 1) / i]

Where:

FVoa = Future Value of an Ordinary Annuity
PMT = Amount of each payment
i = Interest Rate Per Period
n = Number of Periods

FVoa = PMT [((1 + i)^n - 1) / i]
= 50,000 [((1 + 0.04)^20 - 1) / 0.04]
= 50,000 [((2.191123 - 1)/0.04]
= 50,000 * 29.778
=$ 1,488,903.929

In order to know the interest earned on the ...

Solution Summary

The solution discusses the time value of money, including lottery winnings, home shopping and investing in Roth IRA.

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