FNAN 300 Ch. 5
An investment offers a perpetual cash flow of $100 every year. The required return on this investment is 10%. Which of the following is the value of this investment?
$1,000 (100/.10)
The future value of an annuity due of $100 per year for 10 years at 10% is
$1,648.06 100{(1.10^10)/.10}[1.10] This is an annuity due. In the financial calculator, either change the calculator to beginning mode or multiply the ordinary annuity value by (1+r).
Assume $100 earns stated 10% rate compounded quarterly. What will the value of the $100 be after one year?
$110.38 [$100 X (1 X .10/4)^4
You have $2,000 right now that you plan to invest in an account paying 8% interest. You plan to add $1,000 to this account every year, beginning next year, for 10 years. What is the future value of this investment?
$18,804.41 Use Calculator ( 1000 is PMT, 2000 is PV)
Alice has $20,000 in an account that pays 8% per year. Alice wants to withdraw equal amounts at the end of the next 10 years. How much will Alice receive each year?
$20,000 / {1-(1/1.08^10)} /.08
The difference between the present value of an ordinary annuity with payments of $100 per year 10% compounded Annually for 10 years and an annuity due with payments of $100 year 10% compounded annually for 10 years is:
$61.45 ($675.90-$614.45)
What is the present value of an annuity that makes payments of $100/ year for ten years if the first payments is made immediately and the discount rate is 10 percent per year?
$675.90
Suppose you paid a $1,200 loan off by paying $400 in principal each year plus 10% yearly interest. How much is the second interest payment?
$80 ($1,200 -400= 800. x 10%)
Annuity Factor Formula
(1 + r) ^t -1 / r
General Formula for EAR, where M is the number of times interest is compounded in a year?
(1+quoted rate/ m^m)-1
The formula for the present value of an annuity due is:
(1+r)x(PV of an ordinary annuity)
Ways to amortize a loan
1. Pay principal and interest every period in a fixed payment. 2. Pay the interest each period plus some fixed amount of the principal
If the quoted interest rate is 2% per month, what is APR?
24% (2X12)
You borrow $100 and agree to pay back your payday loan in 2 weeks for 10% interest over that 2-week period. What is your stated annual interest rate?
260%
Given an annuity that has a payment of $35 per year, an annual interest rate of 3%, and a present value of $130, it will last for ___ years
4 (Use calculator)
Which of the following is the simplest form of a loan?
A pure discount loan
The interest rate changed per period multiplied by the number of periods per year is equal to _ _ _ on a loan .
Annual Percentage Rate
An annuity with payments beginning immediately rather than at the end of the period is called an ____.
Annuity Due
An annuity due is a series of payments that are made
At the beginning of each period
EAR takes into account the ____ of interest that occurs within a year.
Compounding
The interest rate expressed as if it were compounded once per year is called the ______.
Effective Annual Rate (EAR)
If the interest rate is greater than 0, the value of an annuity due is always ___ an ordinary annuity.
Greater than
More frequent compounding leads to:
Higher EARs
A perpetuity is a constant stream of cash flows for a___ period of time.
Infinite
The present value of an annuity due is equal to the present value of____ annuity multiplied by (1+r)
Ordinary
The entire principal of an interest- only loan is the:
Original loan Amount
C/r is the formula for the present value of an
Perpetuity
The present value formula for a(n)_____is PV=C/r where C is the constant and regularly timed cash flow to infinity, and r is the interest rate.
Perpetuity
Suppose you expect to receive 5,000 in one year, 4,300 in two years and an additional 5,000 in three years. Match each present value amount to the corresponding cash flow assuming a discount rate of 17%.
Present Value of the Year 1 Cash Flow = $4.273.50 ($5,000/1.17) Present Value of Year 2 Cash Flow=$3,141.21 ($4,300/ 1.17^2 Present Value of Year 3 Cash Flow=$3,121.85 ($4,300/ 1.17^3
with typical interest -only loans, the entire principal is:
Repaid at some point in the future
An interest rate expressed in terms of the interest payment made each period is called a ____
Stated Interest Rate Quoted Interest Rate
Because of_____and ______, interest rates are often quoted in many different ways
Tradition, legislation
Perpetuity
a constant stream of cash flows forever
The Most common way to repay a loan is to pay
a single fixed payment every period
