Time Value of Money
1. (Number of Period) Suppose you want to buy a new house. You currently have $15,000, and you figure you need to have a 10% down payment plus an additional 5% of the loan amount for closing costs. Assume the type of house you want will cost about $150,000 and you can earn 7.5% per year. How long will it be before you have enough money for the down payment and closing costs?
2. (EAR) A pro-football team offers one of its players the choice between the following contracts:
a. Yearly salary (payable at the end of every year) of $400,000 for 5 years;
b. Quarterly salary (payable at the end of every quarter) of $95,000 for 5 years?
c. monthly salary (payable at the beginning of every month) of $31,000 for 5 years?
Assuming the APR quoted is 8% compounded semi-annually, which contract should this player accept? Show all your calculations
3. (Perpetuity) You want to endow a chair for a female professor of finance. You'd like to attract a prestigious faculty member, so you'd like the endowment to add $100,000 per year to the faculty member's resources (salary, travel, databases, etc.) If you expect to earn a rate of return of 4% annually on the endowment, how much will you need to donate to fund the chair?
4. (Growing Annuity) You want to begin saving for your retirement. You plan to contribute $12,000 to the account at the end of this year. You anticipate you will be able to increase your annual contributions by 3% each year for the next 45 years. If your expected annual return is 8%, how much do you expect to have in your retirement account when you retire in 45 years?
5. (Comprehensive) A man aged 40 wishes to accumulate a fund for retirement by depositing $1,000 at the beginning of each year for 25 years. Starting at age 65, he will make 15 annual withdrawals at the beginning of each year. Assuming that all payments are certain to be made, find the amount of each withdrawal starting at age 65 if the annual interest rate (compounded annually) is 4% during the first 25 years but only 3.5% thereafter.