i. Find the future values of the following ordinary annuities
FV of $400 each 6 months for 5 years at a nominal rate of 12%, compounded semiannually
FV of $200 each 3 months for 5 years at a nominal rate of 12%, compounded quarterly
The annuities described in parts a and b have the same total amount of money paid into them during the 5-year period, and both earn interest at the same nominal rate, yet the annuity in part b earns $101.75 more than the one in part a over the 5 years. Why does this occur?
ii .What is the present value of a perpetuity of $100 per year if the appropriate discount rate is 7%? If interest rates in general were to double and the appropriate discount rate rose to 14%, what would happen to the present value of the perpetuity?
iii. Ralph Renner just borrowed $30,000 to pay for a new sports car. He took out a 60-month loan and his car payments are $761.80 per month. What is the effective annual rate (EAR) on Ralph’s loan?
iv. Joe Ferro’s uncle is going to give him $250 a month for the next two years starting today. If Joe banks every payment in an account paying 6% compounded monthly, how much will he have at the end of three years?