Ch 05- Assignment - Time Value of Money - Part 1

Rahul needs a loan and is speaking to several lending agencies about the interest rates they would charge and the terms they offer. He particularly likes his local bank because he is being offered a nominal rate of 4%. But the bank is compounding bimonthly (every two months). What is the effective interest rate that Rahul would pay for the loan?

%4.067

Opportunity cost of Funds

A 6% return that you could have earned if you had made a particular investment.

Annual Percentage rate

A value that represents the interest paid by borrowers or earned by lenders, expressed as a percentage of the amount borrowed or invested over a 12-month period.

Assume that the variables I, N, and PV represent the interest rate, investment or deposit period, and present value of the amount deposited or invested, respectively. Which equation best represents the calculation of a future value (FV) using: Simple Interest?

FV = PV + (PV x I x N)

All other things being equal, the numerical difference between a present and a future value corresponds to the amount of interest earned during the deposit or investment period. Each line on the following graph corresponds to an interest rate: 0%, 10%, or 20%. Identify the interest rate that corresponds with each line.

Line A: 20% Line B: 10% Line C: 0%

An investor can invest money with a particular bank and earn a stated interest rate of 4.40%; however, interest will be compounded quarterly. What are the nominal, periodic, and effective interest rates for this investment opportunity?

Nominal Rate: 4.40% Periodic rate: 1.10% Effective Annual rate: 4.47%

Future value

One of the four major time value of money terms; the amount to which an individual cash flow or series of cash payments or receipts will grow over a period of time when earning interest at a given rate of interest.

Which of the following is true about present value calculations?

Other things remaining equal, the present value of a future cash flow decreases if the investment time period increases.

Time Value of Money

The concept that states that the timing of the receipt or payment of a cash flow will affect its value to the holder of the cash flow.

Discounting

The process of determining the present value of a cash flow or series of cash flows to be received or paid in the future.

Which of the following investments that pay will $5,000 in 12 years will have a higher price today?

The security that earns an interest rate of 5.50%.

All other factors being equal, both the simple interest and the compound interest methods will accrue the same amount of earned interest by the end of the first year.

True

The process of earning compound interest allows a depositor or investor to earn interest on any interest earned in prior periods.

True

The process for converting present values into future values is called _______ . This process requires knowledge of the values of three of four time-value-of-money variables. Which of the following is not one of these variables?

compounding; The inflation rate indicating the change in average prices

Investments and loans base their interest calculations on one of two possible methods: the _____ interest and the ______ interest methods. Both methods apply three variables—the amount of principal, the interest rate, and the investment or deposit period—to the amount deposited or invested in order to compute the amount of interest. However, the two methods differ in their relationship between the variables.

simple; compound

Another bank is also offering favorable terms, so Rahul decides to take a loan of $12,000 from this bank. He signs the loan contract at 5% compounded daily for 12 months. Based on a 365-day year, what is the total amount that Rahul owes the bank at the end of the loan's term? (Hint: To calculate the number of days, divide the number of months by 12 and multiply by 365.)

$12,615.21

Heather deposited $1,700 at her local credit union in a savings account at the rate of 9.8% paid as simple interest. She will earn interest once a year for the next 13 years. If she were to make no additional deposits or withdrawals, how much money would the credit union owe Heather in 13 years?

A = $3,865.80 I = A - P = $2,165.80 Equation: A = P(1 + rt) Calculation: First, converting R percent to r a decimal r = R/100 = 9.8%/100 = 0.098 per year. Solving our equation: A = 1700(1 + (0.098 × 13)) = 3865.8A = $3,865.80 The total amount accrued, principal plus interest, from simple interest on a principal of $1,700.00 at a rate of 9.8% per year for 13 years is $3,865.80.

Now, assume that Heather's credit union pays a compound interest rate of 9.8% compounded annually. All other things being equal, how much will Heather have in her account after 13 years?

A = $5,731.65 A = P + I where P (principal) = $1,700.00 I (interest) = $4,031.65 Calculation Steps: First, convert R as a percent to r as a decimal r = R/100r = 9.8/100r = 0.098 rate per year, Then solve the equation for AA = P(1 + r/n)nt A = 1,700.00(1 + 0.098/1)(1)(13)A = 1,700.00(1 + 0.098)(13) A = $5,731.65 Summary: The total amount accrued, principal plus interest, with compound interest on a principal of $1,700.00 at a rate of 9.8% per year compounded 1 times per year over 13 years is $5,731.65.

Before deciding to deposit her money at the credit union, Heather checked the interest rates at her local bank as well. The bank was paying a nominal interest rate of 9.8% compounded quarterly. If Heather had deposited $1,700 at her local bank, how much would she have had in her account after 13 years?

A = $5,985.09 A = P + I where P (principal) = $1,700.00 I (interest) = $4,285.09 Calculation Steps: First, convert R as a percent to r as a decimal r = R/100r = 9.8/100r = 0.098 rate per year, Then solve the equation for AA = P(1 + r/n)nt A = 1,700.00(1 + 0.098/4)(4)(13)A = 1,700.00(1 + 0.0245)(52) A = $5,985.09 Summary: The total amount accrued, principal plus interest, with compound interest on a principal of $1,700.00 at a rate of 9.8% per year compounded 4 times per year over 13 years is $5,985.09.

Amortized Loan

A loan in which the payments include interest as well as loan principal.

Perpetuity

A series of equal (constant) cash flows (receipts or payments) that are expected to continue forever.

Annuity due

A series of equal cash flows that occur at the beginning of each of the equally spaced intervals (such as daily, monthly, quarterly, and so on).

Ordinary annuity

A series of equal cash flows that occur at the end of each of the equally spaced intervals (such as daily, monthly, quarterly, and so on).

Amortization schedule

A table that reports the results of the disaggregation of each payment on an amortized loan, such as a mortgage, into its interest and loan repayment components.

Eric wants to invest in government securities that promise to pay $1,000 at maturity. The opportunity cost (interest rate) of holding the security is 13.80%. Assuming that both investments have equal risk and Eric's investment time horizon is flexible, which of the following investment options will exhibit the lower price?

An investment that matures in eleven years

Assume that the variables I, N, and PV represent the interest rate, investment or deposit period, and present value of the amount deposited or invested, respectively. Which equation best represents the calculation of a future value (FV) using: Compound interest?

FV = PV x (1 + I)^N

After the end of the second year and all other factors remaining equal, a future value based on compound interest will never exceed the future value based on simple interest.

False

Which of the following is true about finding the present value of cash flows?

Finding the present value of cash flows tells you how much you need to invest today so that it grows to a given future amount at a specified rate of return.

Time value of money calculations can be solved using a mathematical equation, a financial calculator, or a spreadsheet. Which of the following equations can be used to solve for the present value of an annuity due?

PMT x ({1 - [1/(1 + r)^n]}/r) x (1 + r)

Yuri is willing to invest $30,000 for six years, and is an economically rational investor. He has identified three investment alternatives (X, Y, and Z) that vary in their method of calculating interest and in the annual interest rate offered. Since he can only make one investment during the six-year investment period, complete the following table and indicate whether Yuri should invest in each of the investments. x : 11% Compound interest Y : 13% Compound Interest Z 13% Simple Interest

X: A = P(1 + r/n)^nt A = 30,000.00(1 + 0.11/1)^(1)(6) A = 30,000.00(1 + 0.11)^(6) A = $56,112.44 Y: A = P(1 + r/n)^nt A = 30,000.00(1 + 0.13/1)^(1)(6) A = 30,000.00(1 + 0.13)^(6) A = $62,458.55 Z: A = 30000(1 + (0.13 × 6)) = 53400 A = $53,400.00