Question

(TCO 5) Jane’s parents have created a savings account to save for her college education. If they invest $1,000 a year at 6% interest beginning on her first birthday, how much will be in the account when she reaches age 18?

(TCO 5) You own a contract that promises an annuity cash flow of $250 year-end cash flows for each of the next 3 years. (Note: The first cash flow is exactly 1 year from today). At an interest rate of 8%, what is the present value of this contract?

(TCO 5) You have been accepted into a prestigious private university in Illinois for your doctoral program. Congratulations! Since no one from this school has ever graduated in only 4 years, you anticipate that you will need to make 11 semi-annual tuition payments of $35,000 each with the first cash flow 6 months from today. If you choose to discount these cash flows at an annual rate of 8%, what is the present value cost of tuition to attend your university of choice?

(TCO 5) You are about to purchase a new car from a dealer who has a new and unusual payment plan. You have the choice to pay $29,000 cash today or $32,000 in 4 years. If you have the opportunity to borrow the cash price value of the car at a rate of 3.0% and repay the loan in a lump sum in 4 years, which option should you take and why?

(TCO 5) Which choice has a greater present value if we assume a required rate of return of 8%? (1) A lump-sum cash flow today of $248.69 (2) $100 cash flows occurring 1, 2, and 3 years from today (3) A single cash flow of $331 3 years from today

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Answer 1

1. Amount Invested = $1,000; Interest Rate = 6%; Number of years = 18 - 1 = 17years

Future Value at 18years = $1,000 = $2,699.77

Therefore amount in the account when Jane reaches age 18 is $2,699.77

2. Annuity Cash flow = $250; Period = 3 years; Interest Rate = 8%

Present Value of the cashflow is $644.27

or we can use the present value of an annuity formula of P((1-(1+r)^-n)/r),

we would use, 250((1-(1+0.08)^-3)/0.08) = $644.27

3. Installment amount of tution payment = $35,000; Term = 11 periods; Interest per term = 4%

Present Value of the cashflow is $306,616.68

or we can use the present value of an annuity formula of P((1-(1+r)^-n)/r),

we would use, 35000((1-(1+0.04)^-11)/0.04) = $306,616.68

The present value of all the tution payments would be $306,616.68

4. If we opt to pay in future, we would pay $32,000 after 4 years.

If we take a loan of cash price of $29,000, we would pay the lumpsum in 4 years. Lumpsum payment after 4 years = Future Value of $29,000 at 3% after 4 years

= $29,000(1.03)^4

= $32,639.80

So, if we take a loan of cash price today, we would have to pay more than $32,000. It is preferred to take up the new and unusual scheme offered by the car dealer.

5. Which choice has the greater present value when rate of return is 8%:

a. A lumpsum cash of $248.69 today

b. $100 cash flows occuring 1,2 and 3 years from today = $100 x 2.5771 = $257.71

c. A single cash flow of $331.3 years from today = $331 x 0.7938 = $262.75

Therefore, the greater present value is a single cash flow of $331 3 years from today