Question

Time Value of Money

1. Keenan has won the lottery for $10,000,000. He is offered a cash payment now of $7,500,000, or 10 annual payments of $1,000,000.

• _____________ What is the interest rate that makes these two amounts equal?

• _____________ If you can invest at 8% how much would you have after 10 years if you invested the $7,500,000?

2. You want a new car that costs $32,000. Figure out the following:

• ______________ What would the monthly payment be if you borrowed $32,000 from a credit union at 4% for 5 years?

• ______________ What would be the total of monthly payments (the amount you would actually pay for the car)?

• ______________ How much interest would you pay if you did this?

• ______________ How much would you have to save each month if you decided to save for 5 years and pay cash for the car, and you could earn 6% on your savings?

• ______________ What would be the total of monthly savings (the amount you would actually pay for the car if you saved)?

3. You have a trust that mature to $75,000 that you will receive when you are 40 years old. You are 23 years old now. If the trust is growing at 4% per year what is the value of the trust now? ____________

4. You want to purchase a house that costs $150,000. You have $30,000. Because you have good credit score you have been offered a loan of 15 years at 3% or 30 years at 3.75%.

• ______________ How much is your loan?

• ______________ What is your monthly principal and interest payment for the 15 year loan?

• ______________ What is your monthly principal and interest payment for the 30 year loan?

• _____________ What is the total of the payments (the amount you actually pay for the house) with the 15 year loan?

• _____________ What is the total of the payments (the amount you actually pay for the house) with the 30 year loan?

Answer 1

(1) Lump sum Offering = $ 7500000, Annual Payments = $ 1000000 and Tenure = 10 years

Let the interest rate that makes the two options equal be r%

Therefore, 7500000 = 1000000 x (1/r) x [1-{1/(1+r)^(10)}]

Using EXCEL's Goal Seek Function/hit and trial method/ a financial calculator to solve the above equation, we get:

r = 0.056 or 5.6 %

Initial Investment = $ 7500000, Interest Rate = 8 % and Tenure = 10 Years

Final Value = 7500000 x (1.08)^(10) = $ 16191937.48

NOTE: Please raise separate queries for solutions to the remaining unrelated questions, as one query is restricted to the solution of only one complete question with up to four sub-parts.