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```An Overview of Personal Finance
• The Time Value of Money
– Money received today is worth more that money to be received
in the future
– Interest Rates
• Nominal Rates = Real Rates + Inflation
– Interest Rates are the cost of borrowing or the price charged
for lending money
– Simple Interest – Interest on the initial value only (Not
commonly used)
– Compound Interest – Interest charged on Interest (Typical in
Lending and Savings)
An Overview of Personal Finance
• The Time Value of Money
– Present Value (PV) - a lump sum amount of money
today
– Future Value (FV) - a lump sum amount of money in
the future
– Payment (PMT) or Annuity - multiple sums of
money paid/received on a regularly scheduled basis
An Overview of Personal Finance
• The Six Financial Functions
– Future value of a lump sum invested today
• Compound Growth
• FV = PV(1+i)n
• PV=value today, i= interest rate, & n= time
periods
• Example: where PV= \$1, n=3, & i=10%
– FV = \$1 x (1+.10) x (1+.10) x (1+.10)
– FV = \$1 x 1.331
– FV = \$1.331
An Overview of Personal Finance
• The Six Financial Functions
– Present Value of a Lump Sum
• Discounting
– Process of finding present values from a
future sum
• PV = FV [1/(1+i)n ]
• Example: where FV= \$1, n=3, & i=10%
– PV = \$1 x [1/(1+.10) x (1+.10) x (1+.10)]
– PV = \$1 x [1/1.331]
– PV = \$1 x 0.7513
– PV = \$0.7513
An Overview of Personal Finance
• The Six Financial Functions
– Future Value of an Annuity
• FVA = PMT[((1+i)n -1))/ i]
• The future value of a stream of payments
An Overview of Personal Finance
• The Six Financial Functions
– Present Value of an Annuity
• PVA = PMT[(1-(1/(1+i)n ))/ i]
• The present worth of a stream of payments
An Overview of Personal Finance
• The Six Financial Functions
– Sinking Fund
• SF PMT = FVA [ i / ((1+i)n -1))]
• The payment necessary to accumulate a specific
future value
An Overview of Personal Finance
• The Six Financial Functions
– Mortgage Payments
• MTG PMT = PVA [ i / ((1 - (1/(1+i)n )))]
• The payment necessary to amortize (retire) a
specific present value
An Overview of Personal Finance
• The effect of changing the compounding frequency
– Interest Rates are quoted on an annual basis
– Increasing the frequency of compounding increases
the amount of interest earned
– Increasing the frequency of payments for an
amortizing loan decreases the amount of interest
paid
An Overview of Personal Finance
• A Future Value Example:
amount of \$10,000. You wish to invest the money in a
money market account at the bank which pays 9% per
year (annually). How much will your investment be
worth in 10 years? How about 30 years. Is the effect of
compounding 3 times greater?
An Overview of Personal Finance
• A Present Value Example:
– You have been offered a guaranteed investment which
will pay you \$50,000 at the end of 15 years. This is the
amount you expect to pay to send your child to college.
You need to make a reasonable offer for the investment
so that you can purchase it today. You expect that
similar investments would provide an 8% return per
year (annually). How much should you be willing to
pay (in one lump sum) today for this investment?
An Overview of Personal Finance
• Future Value of an Annuity Example:
– You wish to save \$2,000 per year over your working
life 40 years. You can invest your savings at 8% per
year (annually). How much money will you have in the
account when you retire?
An Overview of Personal Finance
• Present Value of an Annuity Example :
– You will receive \$5,000 per year over the next 20 years
as part of the winnings of a game show in which you
competed. A company wishes to buy this series of
payments from you. You could invest the money at 7%
annually over the time it is paid. How much should you
sell (in one lump sum) the investment for today?
An Overview of Personal Finance
• Sinking Fund Payment Example:
– You wish to buy a house in 5 years. The down payment
on a house, like you hope to purchase, will be \$7,500.
How much must you save every year to afford this
down payment, given that you can invest the savings
with the bank at 8%?
An Overview of Personal Finance
• Mortgage Payment Example:
– You have negotiated the purchase of a condominium for
\$70,000. You will need a loan of \$60,000, which the
local bank has offered based on a 30 year term at 6%
interest (annually). How much will your annual
payment be for the condo?
– Since nearly all mortgages are calculated on a monthly
basis what is the monthly payment for the loan?
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