lecture 2: time value of money Flashcards
using timelines to visualise cash flows
-r=10%
-years: 0,1,2,3,4
-cash flow: whatever numbers
-0- beginning of period one, at two- end of period two and beginning of period 3, at four- end of period two/beginning of period 5
compound interest (definition and how to work out)
-compounding is when interest earned in first period is paid on the principle, then when interest earned in the second period is paid on the new sum (principle and previous interest earned) and so-on
-equation:
-value at end of year= present value (1=r)^n
-r= interest paid, n is number of years
-e.g. at end of year 2: PV(1+r)^2
future value (definition and equations)
-future value is an amount a sum will grow to in a certain amount of years when compounded at a specific rate
-FV=PV(orV0)(1+r)^t
-FV= future value
-r= annual interest (or discount) rate
-t=number of years
-PV=present value/sum originally invested
How to increase future value
-increase number of years you are compounding (t)
-increase the discount rate (r)
-increase sum of original investment (PV)
Present Value (def and equation) and what increase present value
-present value reflects current value of a future payment or a receipt
-equation: PV=FV(1+r)^t
-FV is future value
-t: number of years until payment received
-r: interest rate
-PV: present value
increase PV:
-time period shorter
-interest rate lower
annuities (and ordinary annuities)
-annuities: series of equal dollar payments for a specified number of years
-ordinary annuity is paid at end of each period
FV of annuity (and example)
-compound annuity: depositing an equal sum of money at end of each year for certain number of years and allowing it to grow
-i.e. depositing 500 dollars at 6% for five years:
FV= 500(1.06)^4 +500(1.06)^3+500(1.06)^2+…+500(1.06)^0 (do each separately)
FV of annuity- using mathematical formula
-FVn=PMT(((1+r)^n)-1)/r)
-OMT annuity payment deposited
FV of annuity changing PMT, r and n
-increasing PMT increases FVn
-increase r and n increases payment
present value of an annuity and mathematical formula
-pensions, insurance obligations and interest owed on bonds are all annuities- to compare need to know present value
-PV of annuity= C/r(1-(1/(1+r)^n))
FV of annuities due and example
-ordinary annuity payments shifted forward one year (paid at beginning of period rather than the end)
-multiply by (1+r)
amortized loans
-loans paid off in equal instalments over time
-periodic payment is fixed. however, amount you pay for each payment differ. you keep owing less towards principal and interest paid declines
how to find PMT
rearrange PV of annuity
perpetuity and how to find PV of perpetuity
-annuity that continues forever
-PV (present value of perpetuity)=PP(present value of perpetuity)/r
making interest rates comparable and quoted rates vs effective rates. and how to change N and r
-cannot compare 5% quarterly payment with 5% annual payment
-Annual Percentage rate (APR)= interest rate per period x compounding periods per year (m)
-Effective annual rate (EAR)= (1+(APR/compound periods per year)^m -1
-N=years x compounding
-r=rate/number of compounding
