time value of money

chapter 12

annunity

same amount over an evenly spaced amount of time

discounted at the same interest rate in each period ( a series of consecutive equal periodic elements)

money can grow over time because it can earn interest

Question: would you rather have a $1,000 today or a year from now on ?

answer: today —> worth more today (because it gains interest)

present value

is what an amount in the future is worth today assuming it earns interest at a given compound interest rate

PV

present value

FV

future value

Interest rate

i

present value of amount due in future

PV= 1 / (1 + i)^t x FV

interest rates

always annual

future value

future value is the sum of which an amount will increase as the result of compound interest

future value of an annuity

equal payments are made each period. the payments and interest accumulate over time

future value of an annuity formula

amount x [(1+r)^n -1 / r]

interest earned=

investment balance - initial investment

ex: present value of a $50,000 annuity received over 2 years, assuming a 9% interest ?

A=$50,000

t=2

i=0.09 %

50,000 [1- 1/(1+0.09)²] divided by 0.09

example: one lump-sum payment of $300,000 five years from now

cost capital = 7%

300,000/(1+0.07)^5

single future amount

equal payments of $28,000 at the end of each year (starting one year from today) for 10 years

cost capital of 7%

annuity (equal yearly payments)

what would balance in the investment be in __ years ?

interest earned = investment balance in __ years — initial investment

(last page- page number #4 future value handout)