Exam 5: Time Value of Money

You just inherited some money, and a broker offers to sell you an annuity that pays $5,000 at the end of each year for 20 years. You could earn 5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

Suppose you are buying your first condo for $145,000, and you will make a $15,000 down payment. You have arranged to finance the remainder with a 30-year, monthly payment, amortized mortgage at a 6.5% nominal interest rate, with the first payment due in one month. What will your monthly payments be?

As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal to or less than the nominal rate on the deposit (or loan).

Farmers Bank offers to lend you $50,000 at a nominal rate of 5.0%, simple interest, with interest paid quarterly. Merchants Bank offers to lend you the $50,000, but it will charge 6.0%, simple interest, with interest paid at the end of the year. What's the difference in the effective annual rates charged by the two banks?

Your aunt has $500,000 invested at 5.5%, and she now wants to retire. She wants to withdraw $45,000 at the beginning of each year, beginning immediately. She also wants to have $50,000 left to give you when she ceases to withdraw funds from the account. For how many years can she make the $45,000 withdrawals and still have $50,000 left in the end?

Pace Co. borrowed $20,000 at a rate of 7.25%, simple interest, with interest paid at the end of each month. The bank uses a 360-day year. How much interest would Pace have to pay in a 30-day month?

Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the beginning of each of the next 20 years?

Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the end of each of the next 20 years?

Which of the following statements is CORRECT?

The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan's life, the greater the percentage of the payment that will be a repayment of principal.

What is the PV of an annuity due with 5 payments of $2,500 at an interest rate of 5.5%?

What annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $1,250?

What is the PV of an ordinary annuity with 5 payments of $4,700 if the appropriate interest rate is 4.5%?

You plan to invest in securities that pay 8.0%, compounded annually. If you invest $5,000 today, how many years will it take for your investment to grow to $9,140.20?

Disregarding risk, if money has time value, it is impossible for the future value of a given sum to exceed its present value.

You are considering two equally risky annuities, each of which pays $5,000 per year for 10 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT?

Bob has $2,500 invested in a bank that pays 4% annually. How long will it take for his funds to double?

Your company has just taken out a 1-year installment loan for $72,500 at a nominal rate of 11.0% but with equal end-of-month payments. What percentage of the 2nd monthly payment will go toward the repayment of principal?

Which of the following statements is CORRECT?

You want to buy a new sports car 3 years from now, and you plan to save $4,200 per year, beginning one year from today. You will deposit your savings in an account that pays 5.2% interest. How much will you have just after you make the 3rd deposit, 3 years from now?