SLIDE 5 Interest Rate
Definition
The rate at which your saving/investment grows. It’s
usually quoted as an annual rate, such as 5%.
Simple interest
Means the interest you earned from period one does not
earn interest in period two
Compounding
means the interest you earned from period one can earn
interest in period two.
Compounding Illustrated
- You invest $1,000 today, hold the investment for 3 years, and earn 10%
each year. How much will you accumulate at the end of 3 years?
- With simple interest, you earn $100 each year interest. Total will be $1,300
at the end of the 3 years.
- With annual compounding, $1,331:
__________________________________________ Year Beginning-of- Interest End-of-Year Year Amount Earned Amount 1 $1,000 $100 $1,100 2 1,100 110 1,210 3 1,210 121 1,331
Future Value of Money
Future value is the value in the future of a known amount
today with a stated investment interest rate r for a period of n
FV=Today $ * [(1+r)n]
An example
If you invest $1,000 for 20 years at r=5%, how much will you have in
your account?
Answer: FV = $1,000*[(1+5%)20]=$2,653 You can also use Table A.1 on page 446 in the textbook. Note 5% for
20 years has a future value of 2.6533. That means investing $1 for 20 years at 5% interest rate will become $2.65 (called the future value). Then the future value of investing $1,000 for 20 years is 2.6533*1,000=$2,653.
Future Value of an Annuity
Annuity
Definition: A series of equal payments Example: Saving $1,000 a year for 20 years or receiving
$500 a year for 10 years
Future value of an annuity (a saving schedule)
At 6% annual interest rate, saving $1 a year for 20 years
has a future value of 36.785 (Table A.2, page 448). So the future value of saving $1,000 a year for 20 years is 36.785*1,000=$36,785.
That means if you save $1000 a year at 6% annual interest
rate, it will grow into $36,785 in 20 years.
A Saving Schedule Example - The Power of Compounding
If you save $20 a month at 6% annual after tax
interest rate, you will have
$246.70 in 1 year $1,395.40 in 5 years $3,277.58 in 10 years $9,240.82 in 20 years $20,090.30 in 30 years
Present Value of a Single Payment
Present value is the value today of an amount that would exist
in the future with a stated investment interest rate r (called the discount rate) for a period of n.
PV=Future $ / [(1+r)n]
An example:
You are promised to receive $10,000 in 20 years. At an interest rate
r=5%, what’s the value of that $50,000?
Answer: PV=$10,000/[(1+5%)20]=$3,769 You can also use Table A.3 on page 450 in the textbook. Note 5% for
20 years has a present value of 0.3769. That means $1 in 20 years at 5% discount rate has a present value of $0.3769. Then the present value
- f receiving $10,000 in 20 years is 0.3769*10000=$3,769.