Exam 4: Time Value of Money

Suppose you take out a $10,000 loan at a 6% nominal annual rate. The terms of the loan require you to make 12 equal end-of-month payments each year for 4 years, and then an additional final (balloon) payment of $4,000 at the end of the last month. What will your equal monthly payments be?

Which of the following statements is INCORRECT?

You just deposited $2,500 in a bank account that pays a 12% nominal interest rate, compounded quarterly. If you also add another $5,000 to the account one year (12 months) from now and another $7,500 to the account 2 years from now, how much will be in the account 3 years (12 quarters) from now?

You plan to invest some money in a bank account. Which of the following banks provides you with the highest effective rate of interest?

You agree to make 24 deposits of $500 at the BEGINNING of each month into a bank account. At the end of the 24th month, you will have $13,000 in your account. If the bank compounds interest monthly, what nominal annual interest rate will you be earning?

You want to accumulate $2,500,000 in your RRSP by your retirement date, which is 35 years from now. You will make 30 deposits into your plan, with the first deposit occurring today. The plan's rate of return typically averages 9%. You expect to increase each deposit by 2% as your income grows with inflation. (That is, your second deposit will be 2% greater than your first, the third will be 2% greater than the second, etc.) How much must your first deposit at t = 0 be to enable you to meet your goal?

Last year Toto Corporation's sales were $225 million. If sales grow at 6% per year, how large (in millions) will they be 5 years later?

Your uncle has $500,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $40,000 at the BEGINNING of each year, beginning immediately. How many years will it take to exhaust his funds, i.e., run the account down to zero?

Suppose your credit card issuer states that it charges a 15.00% nominal annual rate. If you must make monthly payments, which amounts to monthly compounding, what is the effective annual rate?

Midway through the life of an amortized loan, the percentage of the payment that represents interest is equal to the percentage that represents principal repayment. This is true regardless of the original life of the loan.

When a loan is amortized, a relatively high percentage of the payment goes to reduce the outstanding principal in the early years, and the principal repayment's percentage declines in the loan's later years.

What is the present value of the following cash flow stream at an interest rate of 12.0% per year: $0 at Time 0; $1,500 at the end of Year 1; $3,000 at the end of Year 2; $4,500 at the end of Year 3; and $6,000 at the end of Year 4?

Your company has just taken out a 1-year installment loan for $72,500. The nominal rate is 12.0%, but with equal end-of-month payments. What percentage of the SECOND monthly payment will go toward the repayment of principal?