FNAN 303 Lecture Notes - Lecture 5: Compound Interest, Annual Percentage Rate, Accrued Interest

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gmubusstudent

15 Mar 2021

School

George Mason University

Department

Finance

Course

FNAN 303

Professor

Ben Drissi Messouak

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Document Summary

Time value of money (tvm) 3 slides 39-54. Compounding matters annually: a given annual stated rate corresponds to a different actual or true annual rate because of compounding. Example to show how compounding works and that it matters. September 30: . 121 (1. 02) = (1. 02)4 = . 243 on. December 31: an 8% loan results in a larger obligation with quarterly compounding than with annual compounding due to interest-on-interest , . 243 vs. . Loans with lower ear have lower costs, all else equal, because ear reflects the true cost of a loan. Investments with higher ear produce more wealth over time, all else equal, because. Ear reflects the true return of an investment. If an interest rate or return is given, assume it is an apr unless told it is an ear or periodic rate. Example: which loan would you (the borrower) prefer if both loans involve receiving.

Related Questions

Loan/deposit products use different compounding frequencies. For example, mortgage, CDs use monthly compounding. Credit cards use daily compounding, even though customers pay interest on a monthly basis. Bonds use quarterly, semiannual or annual compounding. Regardless of compounding frequencies, all the interest rates are quoted per annum (annualized). For example, 4% mortgage rate doesnât mean the borrower pays 4% of the mortgage balance every month. He pays 4%/12 a month. Q1. Have you made any mistakes in the past with the compounding frequency/interest rate quotation? Share your story. Q2. Why do these products use different frequencies? Q3. Why do we quote all the rates per annum?

Problem 1: $3,000 is invested at 7.2% interest. Find the total amount (A) at the end of 5 years if:
a.) Simple interest is earned. (see the "Simple Interest Example" tab)
b.) Interest is compounded annually (see the "Compound Interest Illustration" tab)
c.) Interest is compounded quarterly (see the "Other Compounding Periods" tab)
d.) Interest is compounded monthly (see the "Other Compounding Periods" tab)
Problem 2: A department store charges 12% interest on the unpaid balance of customer charge accounts.
A customer owes $135, and the bill goes unpaid for 4 months. How much will the customer have to
repay after 4 months? Interest is compounded monthly (note that the 12% is an annual rate). (see the "Other Compounding Periods" tab)
Problem 3: A typical family of four spends approximately $600 per month for food. Food costs are
predicted to rise by 4.8% per year for the next 5 years. In five years, how much should
the family budget per month for food? Treat this as compound annual growth. (see the "Compound Interest Illustration" tab)
(assume annual compounding)
Problem 4a: A couple plans to begin saving money for a down payment toward the purchase of a home.
They plan to purchase a home 4 years from now. Right now, home prices are predicted
to rise by 5% per year for the next 5 years. If this prediction is accurate, how much
can this couple expect to pay in 4 years for a home that is currently valued at $210,000?
(what will be the total sales price in 4 years of a home worth $210,000 today?) (see the "Compound Interest Illustration" tab)
Problem 4b: The couple wants to have a 20% down payment on the purchase price in 4 years. Suppose they
have found a mutual fund that earns an average of 8% per year. How much should they invest in the
mutual fund today in order to have enough for a down payment in 4 years?
Assume annual compounding.
(Find the down payment first - that will be their "A" or future value of what they will invest)
(see the "Other Problem Types" tab - we are trying to find the principal or present value to be invested to grow to the down payment amount)
Problem 5: An electric company predicts that the cost of electricity will rise at the rate of 2% per
year for the next ten years. If the average monthly electricity for consumers in this area
is $225, predict the monthly amount that consumers can expect to pay 10 years from now.
(see the "Compound Interest Illustration" tab)

sangriabeetle691

Use a calculator to solve all quantitative problems, and be sure to show calculator format!!!

(n, I, pmt, pv, fv CFo,I,CF1, CF2â¦.)

8) Three years ago a company had sales of $300,000. Now sales are $1,000,000. At what rate have

sales been growing?

9) Define each of the following:

a) Quoted rate (APR)

b) Periodic rate

c) Effective annual rate (EAR)

10) What are the following Effective Annual Rates (EAR) for 12%:

a) Compounded semiannually?

b) Compounded quarterly?

c) Compounded daily?

11) What would the value of $500 be after 4 years, assuming a return of 8% per year:

a) with semiannual compounding?

b) with quarterly compounding?

12)A. You plan to invest in a preferred stock issue that pays a $60 dividend at the end of each year. Based

on market conditions, you want to get a 5% return. What are you willing to pay for this security?

12)A You want to buy a car today!! The used car you are looking at costs $21,500. The car dealer will

charge you 5% interest on the three year car loan you need. You will be borrowing the whole $21,500. What will your car payment be, if you will make monthly payments?

13. Your company has invested $2500 in a vending machine today. You expect the machine to last 10 years and to produce the following after tax cash flows per year:

Year 1 $100

Year2 $250

Year 3 $250

Year 4 $300

Year 5 $300

Year 6 $300

Year 7 $300

Year 8 $300

Year 9 $350

Year 10 $350

If you have a required return on your investment of 7%, did you pay too much for the vending machine?

FNAN 303 Lecture Notes - Lecture 5: Compound Interest, Annual Percentage Rate, Accrued Interest

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