Finance Ch 5

• 1. compound the accumulated balance forward one year at a time or
• 2. calculate the FV of each CF first and then add these up

• 1. Discount back one perios at a timeor
• 2. Calculate the PV individually and add them up

*the amount that you would need today in order to exactly duplicate those future cash flows (for a given discount rate)

a level stream of cash flows for a fixed period of time

Annuity PV = C*(1-PVF/r)

= C*{1-[1/(1+r)^t]/r}

an annuity for which the cash flows occur at the beggining of the month/period

• ex: Leases
• any amount that needs to be prepaid the same amount each period

annuity due value= ordinary annuity value * (1+r)

• two steps:
• 1. calc the PV or FV as though it were an ordinary annuity and 2. multiply your answer by (1+r)

• level of stream of cash flows continues forever
• cash flows are perpetual
• also called consols (in Canada and UK)

PV for a perpetuity = C/r

perpetuity

the interest rate expressed in terms of the interest payment made each period

the interest rate expressed as if it were compunded once per year

(1+ Quoted rate/m)^m - 1

(1+ APR/12)¹² - 1

the interest charged per period multiplied by the number of periods per year

also called nominal rate

• FV = PV * (1+r)¹
• 120 = 100 * (1+r)¹
• 1.20 = (1+r)
• r = .20 or 20%

• APR = .20* 365/18
• APR = 4.0556 or 405.56%

• EAR = (1+quoted rate/m)^m-1
• EAR = (1+.20)^365/18-1
• EAR = 39.3292 or 3,932.92%

• pure discount
• interest only
• amortized

simplest form of loan

borrower received money today and repays a single sum at some time in the future.

very common when the term is short (one year or less)

the borrower pays interest each period and to repay the entire principal (the original loan amount) at some point in the future

(if there is just one period it is the same as a pure discount loan)

lender may require the borrower to repay parts of the loan amount over time. The process of paying off a loan by making regular principal reductions is called amortizing the loan

pay interest plus some fixed amount

common with medium term business loans

most common (cars and homes)- borrower makes a single fixed payment every period

• Ex: 5 yr 9% $5,000 loan
• 5,000 = C * (1-1/1.09⁵)/.09
•           = C * (1-.6499)/.09

• C= 5,000/3.8897
•    = 1,285.46

True

ordinary annuity

EAR = (1+quoted rate/m)^m-1

m= the # of times per year the money is compounded (or the # of payments per year)