Question

1068 TIME VALUE OF MONEY 11. In 1966, the average tuition for 1 year in the MBA program at the University of Chicago was $3,600. Thirty years later, in 1996, the average tuition was $27,400. What is the compound annual growth rate in tuition (rounded to the nearest whole percentage) over the 30-year period? 12. You want to buy a Volvo in 7 years. The car is currently selling for $50,000, and the price will increase at a compound rate of 10% per year. You can presently invest in high-yield bonds earning a compound annual rate 14% per year. How much must you invest at the end of each of the next 7 years to be able to purchase your dream car in 7 years? 13. John deposits $2,000 per year at the end of the year for the next 20 years into an IRA account that pays 6%. How much will John have on deposit at the end of 20 years? 14. In 1976, the average price of a domestic car was $5,100. Twenty years later, in 1996, the average price was $16,600. What was the annual growth rate in the car price over the 20-year period? 15. Suppose you receive $3,000 a year in years 1 through 4, $4,000 a year in years 5 through 9, and $2,000 in year 10, with all the money to be received at the end of the year. If your discount rate is 12%, what is the present value of these cash flows? 16. Tracey deposits $5,000 in a 5-year certificate of deposit paying 6% com- pounded semiannually. How much will Tracey have at the end of the 5-year period? 17. Ken purchases a perpetual investment that pays $90 per year indefinitely beginning 1 year from today. What is the price of this bond if the current discount rate is 7.6%? 18. What would be the future value of a loan of $1,000 for 2 years if the bank offered a 10% interest rate compounded semiannually?

Answer 1

11.

The compound annual growth is calculated below:

$3,600\times \left ( 1+i \right )^{30}=27,400$

$\left ( 1+i \right )^{30}=7.611$

$\left ( 1+i \right )=7.611^{\frac{1}{30}}$

$\left ( 1+i \right )=1.0699$

$i=1.0699-1$

$i=0.0699$

Annual growth is 6.99% or 7% (rounded off).