If you deposit $100 today and $100 in 1 year at an 8% interest rate, how much will you have in 2 years? $224.64
What is the future value of $2,000 deposited at the end of each of the next 5 years at an interest rate of 10%? $12,210.20
What is the present value of an investment that will pay $1,00...
Chapter 5 Discounted Cash Flow
Valuation Review Questions and Correct
Answers
If you deposit $100 today and $100 in 1 year at an 8% interest rate, how much will you
have in 2 years? ✅$224.64
What is the future value of $2,000 deposited at the end of each of the next 5 years at an
interest rate of 10%? ✅$12,210.20
What is the present value of an investment that will pay $1,000 at the end of every year
for the next 5 years assuming a 6% discount rate? ✅$4,212.37
What is an annuity?
2 Types ✅A series of constant, or level, stream of cash flows for a fixed period of time
This is a finite series of equal payments occur at regular intervals
(multiple cash flows that are all the same amount)
2 MOST COMMON TYPES OF ANNUITIES
1) Ordinary Annuity
An annuity where the cash flows occur at the end of each period
2) Annuity Due (only a qualitative question on this)
An annuity where the cash flows occur at the beginning of each period
Note: Unless stated otherwise, you can assume an ordinary annuity.
Ordinary Annuity Timeline & Examples ✅Car loans and home mortgages are
examples of ordinary annuities whereby the loan is taken out at time 0 and the first
payment is then due at the end of each period.
Draw Timeline
Annuity Due Timeline & Examples ✅Most apartment lease arrangements are
examples of an annuity due. The monthly payment is due at the beginning of each
month.
Draw Timeline
Future Value for Annuities - Formula ✅FVannuity = Cash Amount per period * Annuity
Future Value Factor
Breakdown -
, Annuity Future Value Factor - (future value factor -1)/ r
Future Value Factor: (1+r)^t
ORRRR
FVannuities = C* [(1+r)^t -1]/r
How much money will you have when you retire in 40 years if you deposit $2,000 per
year into an account and earn 7.5%? ✅[future value of annuities]
$454,513.04
Present Value for Annuities - Formula ✅PVannuity = Cash amount per period * annuity
present value factor
BREAK DOWN --
Annuity Present Value Factor = (1-Present Value Factor)/r
Present Value factor = 1/(1+r)^t
ORRR
PVannuities = C* {1- [1/(1+r)^t]}/r
How much money do you need to deposit today if you want to receive $2,000 per year
for the next 40 years assuming an interest rate of 7.5%? ✅[Present value of annuities]
= $25,188.82
FV and PV for Annuities - Example (What is the relationship)
How much money do you need to deposit today if you want to receive $2,000 per year
for the next 40 years assuming an interest rate of 7.5%?
How much money will you have in 40 years if you deposit $2,000 per year into an
account and earn 7.5%? ✅PV $25,188.82
FV $454,513.04
NOTE: The relationship between PVa and FVa is (1+r)^t
PVa * (1+r)^t = FVa
Annuity Due
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