Learning Objectives for Section 3'4

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Learning Objectives for Section 3.4
Present Value of an Annuity Amortization

• After todays lesson you should be able to
• calculate the present value of an annuity.
• calculate the payment for a loan.
• implement a strategy for solving mathematics of
  finance problems.

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General Formula

• Present Value of an Ordinary Annuity

• PV present value of all payments
• PMT periodic payment
• i interest rate per period
• n total number of payments

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General Amortization Formula

• Present Value of an Ordinary Annuity (solved for
  PMT)

• PV present value of all payments
• PMT periodic payment
• i interest rate per period
• n total number of payments

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Amortization Problem

• Example A bank loans a customer 50,000 at 4.5
  interest per year to purchase a house. The
  customer agrees to make monthly payments for the
  next 15 years for a total of 180 payments.
• How much should the monthly payment be if the
  debt is to be retired in 15 years?
• How much did the customer pay for the loan
  overall?
• How much interest did the customer pay?

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Amortization Problem

• Example A bank loans a customer 50,000 at 4.5
  interest per year to purchase a house. The
  customer agrees to make monthly payments for the
  next 15 years for a total of 180 payments.
• How much should the monthly payment be if the
  debt is to be retired in 15 years?

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Amortization Problem

• Example A bank loans a customer 50,000 at 4.5
  interest per year to purchase a house. The
  customer agrees to make monthly payments for the
  next 15 years for a total of 180 payments.
• b) How much did the customer pay for the loan
  overall?

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Amortization Problem

• Example A bank loans a customer 50,000 at 4.5
  interest per year to purchase a house. The
  customer agrees to make monthly payments for the
  next 15 years for a total of 180 payments.
• c) How much interest did the customer pay?

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Example
Example If you buy a computer directly from the
manufacturer for 3,500 and agree to repay it in
60 equal installments at 1.75 interest per month
on the unpaid balance, how much are your monthly
payments? How much total interest will be paid?
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Example
Example A family is thinking about buying a new
house costing 120,000. The family must pay 20
down, and the rest is to be amortized over 30
years in equal monthly payments. If interest is
at 7.5 compounded monthly, what will the
familys monthly payment be? How much total
interest will be paid over 30 years?
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Refinancing Example
Example A person purchased a 200,000 home 20
years ago by paying 20 down and signing a
30-year mortgage at 13.2 compounded monthly.
Interest rates have dropped and the owner wants
to refinance the unpaid balance by signing a new
10-year mortgage at 8.2 compounded monthly. How
much interest will refinancing save?
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Strategy for Solving Mathematics of Finance
Problems

• Step 1. Determine whether the problem involves a
  single payment or a sequence of equal periodic
  payments.
• Simple and compound interest problems involve a
  single present value and a single future value.
• Ordinary annuities may be concerned with a
  present value or a future value but always
  involve a sequence of equal periodic payments.

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Strategy(continued)

• Step 2. If a single payment is involved,
  determine whether simple or compound interest is
  used. Simple interest is usually used for
  durations of a year or less and compound interest
  for longer periods.
• Step 3. If a sequence of periodic payments is
  involved, determine whether the payments are
  being made into an account that is increasing in
  value -a future value problem - or the payments
  are being made out of an account that is
  decreasing in value - a present value problem.
  Remember that amortization problems always
  involve the present value of an ordinary annuity.

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Strategy(continued)

• Note Be aware that some problems may use more
  than one of these formulas.