Exam 4: Time value of money

At the end of 10 years, which of the following investments would have the highest future value? Assume that the effective annual rate for all investments is the same and is greater than zero.

You just deposited $2, 500 in a bank account that pays a 4.0% nominal interest rate, compounded quarterly.If you also add another $5, 000 to the account one year (4 quarters)from now and another $7, 500 to the account two years (8 quarters)from now, how much will be in the account three years (12 quarters)from now?

You are offered a chance to buy an asset for $7, 250 that is expected to produce cash flows of $750 at the end of Year 1, $1, 000 at the end of Year 2, $850 at the end of Year 3, and $6, 250 at the end of Year 4.What rate of return would you earn if you bought this asset?

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

If the discount (or interest)rate is positive, the future value of an expected series of payments will always exceed the present value of the same series.

Which of the following statements is CORRECT?

The going rate of interest on a 5-year treasury bond is 4.25%.You have one that will pay $2, 500 five years from now.How much is the bond worth today?

Billy Thornton 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 Billy have to pay in a 30-day month?

Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods.

Your business 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?

Suppose you borrowed $12, 000 at a rate of 9.0% and must repay it in 4 equal installments at the end of each of the next 4 years.How large would your payments be?

Time lines can be constructed in situations where some of the cash flows occur annually but others occur quarterly.

You are considering investing in a European bank account that pays a nominal annual rate of 18%, compounded monthly.If you invest $5, 000 at the beginning of each month, how many months would it take for your account to grow to $250, 000? Round fractional months up.

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

A "growing annuity" is any cash flow stream that grows over time.

Your uncle just won the weekly lottery, receiving $375, 000, which he invested at a 7.5% annual rate.He now has decided to retire, and he wants to withdraw $35, 000 at the end of each year, starting at the end of this year.What is the maximum number of whole payments that can be withdrawn before the account is exhausted, i.e., before the account balance would become negative? (Hint: Round down to the nearest whole number.)

S.Treasury bond will pay a lump sum of $1, 000 exactly 3 years from today.The nominal interest rate is 6%, semiannual compounding.Which of the following statements is CORRECT?

Suppose you are buying your first home for $145, 000, and you have $15, 000 for your 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?

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

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