amortization and advanced topics ch 4 Flashcards
What is the formula for calculating monthly payments toward a loan?
PMT = [P × r × (1 + r)^N] / [(1 + r)^N - 1].
What does N represent in the formula for loan payments?
The total number of payment periods.
What is the effective annual rate (EAR)?
The annualized return accounting for compounding frequency.
Write the formula for EAR.
EAR = [(1 + APR/M)^M] - 1.
What is the difference between EAR and nominal interest rate?
EAR accounts for compounding, while nominal does not.
Define a growing perpetuity.
A perpetuity where payments grow at a constant rate indefinitely.
Write the formula for the present value of a GROWING perpetuity.
PV = PMT / (r - g).
What does g represent in the growing perpetuity formula?
The growth rate of payments.
What is the difference between annuities and growing annuities?
Annuities have fixed payments; growing annuities have payments that grow at a constant rate.
Define fractional time periods.
Non-whole time periods used in financial calculations (e.g., days or months).
What is the formula for FV with fractional time periods?
FV = PV × (1 + r)^N.
What is the significance of compounding frequency in EAR calculations?
Higher compounding frequencies result in a higher EAR.
How do you calculate the future value with continuous compounding?
FV = PV × e^(r × t).
What is Euler’s number (e)?
A mathematical constant approximately equal to 2.718.
Define amortization.
The process of paying off a loan in equal installments over time, covering both interest and principal.
What is an amortization schedule?
A table detailing each loan payment, showing portions for interest, principal, and remaining balance.
What happens to interest and principal portions over time in amortization?
Interest decreases, while principal increases with each payment.
What is continuous compounding?
Interest is compounded infinitely many times in a period.
Write the formula for the real rate of return.
Real Rate = [(1 + Nominal Rate) / (1 + Inflation)] - 1.
How is PV affected by increasing the discount rate?
A higher discount rate reduces the present value.
