Interest and

1
Chapter 9 Personal Finance
9.3
Interest and Annuities
9.3.1
MATHPOWERTM 11, WESTERN EDITION
2
Simple Interest
Interest is the rent paid for the use of someone
elses money. The rate at which this interest is
paid is expressed as a percentage of the amount
of money loaned per unit of time. This amount of
money loaned is called the principal.
Interest Principal x Rate x Time
The total sum of money repaid, principal plus
interest is called the amount.
Amount Principal Interest
9.3.2
3
Calculating Simple Interest
A boat motor costs 2500. Mr. Wilson pays
1700 down and the balance at the end of 4 months
with a service charge of 24 per annum simple
interest. What amount must he pay at the end of
the 4 months?
Amount financed
2500 - 1700 800
I PRT
Simple Interest
I 800 x 0.24 x
I ? P 800 R 24 T
64
Mr. Wilson will pay 64 in simple interest,
making his payment amount 864.00
9.3.3
4
Compound Interest
Compound interest is when an amount of money, P
(principal), is invested at an interest rate, i,
compounded annually. The accumulated amount,
A, is given by the formula, A P(1 i)n.
Calculating Compound Interest
Determine the accumulated amount of 6800
invested at 6.75/a compounded annually for 15
years.
A P(1 i)n 6800(1 .0675)15 18
114.53
A ? P 6800 i 6.75 n 15
The accumulated amount is 18 114.53.
9.3.4
5
Calculating Compound Interest
Note that there are two variables that will be
affected by how the interest is compounded - the
i (the interest rate) and the n (the number of
compounding periods).
Interest is given to you as a yearly amount. for
example, 12 per annum. So, when you are
compounding it semiannually, you are dividing
this amount into two parts 6 for the first part
and 6 for the second.
For of periods (n)
Interest
For interest (i)
Multiply by 1 Multiply by 2 Multiply by
4 Multiply by 12 Multiply by 365
Divide by 1 Divide by 2 Divide by 4 Divide by 12
Divide by 365
Annual Semi-annual Quarterly Monthly Daily
9.3.5
6
Calculating Compound Interest
Paul invested 12 000 in an account with an
interest rate of 11/a compounded semi-annually.
How much will he be able to withdraw in 5 years?
A ? P 12 000 i 11 2
A P(1 i)n 12000(1 0.055)10 20
497.73
Since there are 2 interest periods per year.
Since there are 5 x 2 10 periods in 5 years.
n 10
Paul could withdraw 20 497.73 in 5 years.
9.3.6
7
Comparing Compound and Simple Interest
You have 5000 you wish to deposit. Bank A pays
12 simple interest per annum. Bank B pays 10
compounded quarterly. If you plan to invest your
money for 10 years, which bank would give you
the best return? Calculate the difference in the
amount of interest paid.
Bank A
Bank B
I PRT 5000 x 0.12 x 10 6000
A P(1 i)n 5000(1 0.025)40 13
425.32
A P I 5000 6000 11 000
I A - P 13 425.32 - 5000 8425.32
Bank B will pay the greater amount of interest
by 8425.32 - 6000 2425.32.
9.3.7
8
Comparing Banking Options
A bank offers an interest rate of 8 per year
compounded annually. A second bank offers an
interest rate of 8 per year, compounded quarterly
. If 2000 were deposited for 10 years in each
bank, which bank would give the better return
and by how much?
Bank B
Bank A
A P(1 i)n 2000(1 0.02)40
4416.08
A P(1 i)n 2000(1 0.08)10
4317.85
Bank B would have the better return by 4416.08
- 4317 .85 98.23.
9.3.8
9
Loan Payments and Spreadsheets
A loan of 5000 carries an interest rate of 9
per year, compounded monthly. Adele makes
payments of 350 per month. Determine how much
she still owes after making 12 payments.
9.3.9
10
Annuities
An annuity is an investment plan in which fixed
amounts of money are deposited or paid out at
regular intervals over a specified period of
time.
Paul invests 1000 every 6 months, beginning in
Oct., at 6/a compounded semi-annually. How much
will he have at the end of 2 a?
1000
1000(1 0.03)4
1000
1000(1 0.03)3
1000
1000(1 0.03)2
1000
1000(1 0.03)1
1000(1 0.03)4 1000(1 0.03)3 1000(1
0.03)2 1000(1 0 .03)1 1125.51 1092.73
1060.90 1030.00 4309.14
9.3.10
11
Using a spreadsheet
6-month period
Amount
Principal
Interest
9.3.11
12
Assignment
Suggested Questions
Pages 542 and 543 1-4 5-29 odd, 34, 36, 37
9.3.12