Finance Ch 6
Annual Percentage Rate (APR)
the interest rate charged per period multiplied by the number of periods per year -APR is normally less than EAR. -APR of 18% is .18/12=1.5% per month - EAR is =19.56% is what you actually pay
Amortized Loan
the lender may require the borrower to repay parts of the loan over time
Formula for PV of an annuity due:
(1+r) x (PV of an ordinary annuity)
Present Value of Growing Annuity
(C/r-g) x 1- (1+g/1+r)^t
Effective Annual Rate (EAR)
- to compare different investments or interest rates
How to calculate FV for multiple cash flows
-calculate the FV of each CF first then add them up -compound the accumulated balance forward one year at a time
Examples of what should be valued using a perpetuity formular
-cash flows from a product whose sales are expected to remain constant forever -a consol (bond that pays interest only and does not mature) -preferred stock
What is true about a growing annuity?
-cash flows grow at a constant rate -cash flows grow for a finite period
Ways to calculate a balloon payment?
-find the PV of the payments remaining after the loan term -amortize the loan over the loan life to find the ending balance
What payment methods amortizes a loan?
-fixed payments that result in a zero loan balance -interest plus fixed amount
Examples of annuities
-installment loan payments -monthly rent payments in a lease
Real world examples of annuities
-pensions -mortgages
Whats true about a partial amortization loan?
-the amortization period is longer than the loan period -the monthly payment is based on a longer amortization period than the maturity of the loan. -the borrower makes a large balloon payment at the end of the loan period -the monthly payments do not fully pay off the loan by the end of the loan period.
present value interest factor
1- (1/(1+r)^t) /r
Annuity
A level stream of cash flows for a fixed period of time
Interest Only Loan
A loan that only requires the payment of interest for a stated period of time with the principal due at the end of the term or in sometime in the future.
amortization schedule
A schedule that details each loan payment's allocation between principal and interest and the beginning and ending loan balances.
PV of Growing Perpetuity
C/(r-g)
A 12% annual interest rate is compounded semiannually on a $500 investment. What will it be worth after one year?
Find EAR of 12% (1+ (.12/2))^2 -1 enter as I/y PV -$500 n=1 $561.80
Want to fund an account that will pay out $100 per year forever. Inflation will equal 3% per year and expect the account to earn 7% per year. How much do you need to put in the account today?
Growing perpetuity PV=C/(r-g) PV=100/(.07-.03) =$2500 today
Find the FV of an annuity of $100 per year for 10 years at 10% per year
PMT=-100 N=10 I=10 CPT FV $1593.74
What is the PV formula for a perpetuity?
PV=C/r where C is the constant/regularly timed cash flow to infinity r is the interest rate
Stated interest rate
The interest rate expressed in terms of the interest payment made each period. Also known as the quoted interest rate.
APR
The interest rate per period multipled by the number of periods in the year.
EAR
The interest rate stated as though it were compounded once per year.
Balloon Payment
The remaining balance, at maturity, on a loan that has not been completely repaid through periodic payments. Once paid, the outstanding balance is zero. Partially amortized loan.
Because of _______ and ________, interest rates are often quoted in many different ways
Tradition legislation
Consol
a type of perpetuity
perpetuity
an annuity in which the cash flows continue forever
annuity due
an annuity whose payments occur at the beginning of each period
When calculating the FV of multiple CFs you must
calculate the FV of each CF then add the compounded values together
When calculating the PV of multiple CFs you must
calculate the PV of each CF then add the discounted values together
When the interest rate is greater than zero, the value of an annuity due is always ___________ an ordinary annuity
greater than
A single cash flow is known as
lump sum
Simplest form of loan?
pure discount loan
pure discount loan
simplest form of loan; the borrower receives money today and repays a single lump sum at some time in the future
