Ch 4 - Time Value of Money
For multiple period compounding, what is compound interest?
Compound interest is interest that is reinvested (added to principal) and your interest also earns interest.
Compounding more frequently means we are what?
We are paid interest more frequently
What is an ordinary annuity?
A cash flow stream in which an equal flow (payment) occurs at the end of every period for n periods.
What is a deferred annuity?
A deferred annuity is a constant cash flow that starts x years from today.
What is a growing annuity?
A growing annuity is an annuity that increases or decreases by a fixed percentage every year. So each payment is x% larger or smaller than the last.
What is an amortized loan?
A loan repaid in equal payments over its life where the payments include interest and principal
What is a lump sum?
A single cash flow at one point in time .. also called an amount
What is a perpetuity?
An annuity that has no end point.
What is annuity due and what's the formula?
Annuity due describes a payment stream where the first payment is today. Formula is: PVAD = Pmt / r x [ 1 minus (1 / 1+ r)N ] x (1+r)'
What is N' and what is the formula?
Any number of sub annual time periods. N' = N x m
What is EAR?
EAR is the effective annual interest rate. It is the rate of annually compounded interest that is equivalent to some nominal rate of compounded more frequently.
How would you calculate the ending balance?
Ending balance = Beginning balance minus Principal Reduction
What is the FV of growing annuity formula?
FV = Pmt1 / r minus g x [(1+r)n minus (1+g)N]
What are the compound frequencies for annual, semi annual, quarterly, monthly, weekly, and daily?
For annual: 1, semi annual: 2, quarterly: 4, monthly: 12, weekly: 52, daily: 250, 360, 365
If i and n increases, the future value _____. Why does this happen?
Future value increases. When interest rate increases, future value increases because you earn more interest and more interest is reinvested which leads to increase in future value. As number of years increases, future value increases because as number of years increases, we have more compounding and receive more interest.
What is the future value with uneven cash stream formula?
Future value with uneven cash stream = FV = PV x (1+r)N + PV x (1+r)N ....
What risk level does a small stock have?
High risk level
How would you calculate interest?
Interest = Beginning Balance x r'
What risk level does a government bond have?
Low risk level
When dealing with savings and withdrawals, what should I do?
Make a timeline
What risk level does a large stock have?
Medium risk level
For multiple period compounding, what is simple interest?
Simple interest is when you only earn interest on the principal
How would you find the payment?
Use the standard annuity formula
What risk level does a start up have?
Very high risk level
What risk level does a bank CD investment have?
Zero risk level
m is?
m is the number of times that interest is compounded
What does the payments equation look like?
Payments = Principal Reduction + Interest
How can you solve for the deferred annuity amount or the present value of the deferred annuity amount?
2 ways ... you can use the PV ordinary annuity equation and solve for the PV, and the PV will be the one period before the annuity starts. Then you just convert this PV/FV of the one period before the annuity starts to a present value number to what it should be today. Another way is to use the annuity due formula and this will give the PV/FV of when the annuity starts and then just convert it to a present value to what it's supposed to be today.
What is r' and what is the formula?
Any sub annual discount rate. R' = APR / m
Stated annual rate is known as?
As APR or Annual Percentage Rate
How does i and n affect present value?
As i increases, I earn more interest so I need less today (decrease in present value). As n increases, you have more time which means more compounding (need less to get there ... which means decrease in present value)
What is the net present value of a cash flow stream equation?
Net Present Value (NPV) = PV of benefits minus PV of costs
What does PV, FV, N, and r/i mean?
PV stands for present value and is the value of cash flow today, FV stands for future value and is the value of cash flow at time N, N is the number of years or time, r is the interest rate .. what the investment earns.
What is the present value with uneven cash stream formula?
Present value with uneven cash stream = FV1 / 1 + r + FV2 / (1+r)2 + ....
How would you calculate principal reduction?
Principal Reduction = Payment minus interest
