TIME VALUE OF MONEY

Practices

Question 1

Your company is planning to borrow $500,000 or a 5-year, 7%, annual payment fully amortized term loan. Write the loan amortization schedule. What fraction of the payment mode at the end of the second year will represent repayment of principal?

Question 2 (CFA level1)

Two years from now, a client will receive the first of three annual payments of $20,000 from a small business project. If she can earn 9% annually on her investments and she plans to retire in six years. How much will the three business project payments be worth at the time of her retirement?

Question 3

Your firm can borrow from its bank for one month. The loan will have to be “rolled over” at the end of the month, but you are sure the rollover will be allowed. The nominal interest rate is 14%, but interest will have to be paid at the end of each month, so the bank interest rate is 14%, monthly compounding. Alternatively, your firm can borrow from an insurance company at a nominal rate that would involve quarterly compounding. What nominal quarterly rate would be equivalent to the rate charged by the bank?

Question 4

You plan to buy a new HDTV. The dealer offers to sell the set to you on credit. You will have 3 months in which to pay, but the dealer says you will be charged a 15% interest rate; that is, the nominal rate is 15%, quarterly compounding. As an alternative to buying on credit, you can borrow the funds from your bank, but the bank will make you pay interest each month. At what nominal bank interest rate should you be indifferent between the two types of credit?

Question 5

The Wade family is interested in buying a home. The family is applying for a $200,000 30-year mortgage. Under the terms of the mortgage, they will receive $200,000 today to help purchase their home. The loan will be fully amortized over the next 30 years. Current mortgage rates are 7.5%. Interest is compounded monthly and all payments are due at the end of the month.

Question 6

Janet has been given $15,000 by her grandparents today on their 21st birthdays. She wants to save for her future and has aspirations of one day being millionaires. She plans to make annual contributions on her birthday, beginning next year. Janet has opened investment accounts at the 1st National Bank and she expects to earn nominal returns of 6%. Janet has already decided to deposit $7,500 each year into her investment account. How many years will it take Janet before she reaches her investment goal of $1 million?

Question 7

Henry has saved $5,000 and intends to use his savings as a down payment on a new car. After careful examination of his income and expenses, Henry has concluded that the most he can afford to spend every month on his car payment is $425. The car loan that Henry uses to buy the car will have an APR of 10%.

Question 8

Assume that you have $15,000 in a bank account that pays 5% annual interest. You plan to go back to school for a combination MBA/law degree 5 years from today at Harvard Business School. It will take you an additional 5 years to complete your graduate studies. You figure you will need a fixed income of $25,000 in today’s dollars; that is, you will need $25,000 of today’s dollars during your first year and each subsequent year. (Thus, your real income will decline while you are is school.) You will withdraw funds for your annual expenses at the beginning of each year. Inflation is expected to occur at the rate of 3% per year. How much must you save during each of the next 5 years in order to achieve your goal? The first increment of savings will be deposited one year from today.