Unformatted text preview: Mathematics of Finance Compound Interest INTEREST Mathematics: Applications for Business SIMPLE INTEREST COMPOUND INTEREST Compound Interest is interest paid on interest already earned as well as
on principal.
Suppose that some principal amount is deposited at interest rate r per
year. The interest for the next year is paid on the total amount on deposit
at the end of the previous year.
Year Principal Based on custom edition “Math: Applications for Business.”
Prepared and summarized by Vera Klimkovsky. Future Amount Mathematics of Finance Compound Interest The Compound Amount is the total amount on deposit after t years. Compound Amount Formula:
Note:
This formula is used when interest
is compounded annually (i.e. once
a year) is the principal.
is the rate of interest per year.
is a number of years. Example:
A small business borrows $50,000 for expansion at 12% compounded
annually. The loan is due in 4 years. How much interest will the business
pay? Mathematics: Applications for Business Solution: Based on custom edition “Math: Applications for Business.”
Prepared and summarized by Vera Klimkovsky. Mathematics of Finance Compound Interest Compounding periods
Interest may be compounded more than once a year: Semiannually (twice per year)
Quarterly (four periods per year)
Monthly (twelve periods)
Daily (usually 365 periods per year) Compound Amount Formula:
Note:
This formula is used when interest
is compounded more than once a
year. is a number of compounding
periods. Mathematics: Applications for Business Example:
A developer needs $80,000 to buy land. He is able to borrow the money
at 10% per year compounded quarterly. How much will the interest
amount to if he pays off the loan in 5 years?
Solution: compounding periods per year. Based on custom edition “Math: Applications for Business.”
Prepared and summarized by Vera Klimkovsky. Mathematics of Finance Compound Interest Then,
and Mathematics: Applications for Business ( ) Continuous Compounding
Formula:
Note:
This formula is used when interest
is compounded continuously (i.e. at
every given moment in time) ( ) Example:
Suppose $10,000 is invested at an annual rate of 5% for 10 years. Find
the future value if interest is compounded as follows.
(a)
(b)
(c)
(d)
(e) annually,
quarterly,
monthly,
daily, and
continuously. Based on custom edition “Math: Applications for Business.”
Prepared and summarized by Vera Klimkovsky. Mathematics of Finance Compound Interest Solution:
, , . a) annually m = 1
b) quarterly, m = 4
c) monthly, m = 12
d) daily, m = 365
e) continuously
Practice Exercises
1. Find the compound amount for the following deposit:
$470 at 10% compounded semiannually for 12 years. Mathematics: Applications for Business 2. Find the amount of interest earned by the following deposit:
$5124.98 at 6.3% compounded quarterly for 5.2 years.
3. Find the compound amount if $25,000 is invested at 6%
compounded continuously for 15 years.
4. Find the present value of the following future amount:
$4253.91 at 6.8% compounded semiannually for 4 years.
Applications
Problem
Bill Poole wants to have $20,000 available in 5 years
for a down payment on a house. He has inherited
$15,000. How much of the inheritance should he
invest now to accumulate the $20,000, if he can get
an interest rate of 8% compounded quarterly? Based on custom edition “Math: Applications for Business.”
Prepared and summarized by Vera Klimkovsky. ...
View
Full
Document
This note was uploaded on 10/19/2011 for the course MATH 110 taught by Professor Staff during the Spring '11 term at S.F. State.
 Spring '11
 Staff
 Math, Calculus

Click to edit the document details