Section F.1, F.2, F.3
MATH 166:503
March 24, 2015
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FINANCE
1.1
Simple Interest and Discount
Def: the principal (or present value) is
Def:
ex. Suppose you put $1000 in a bank account earning .5% simple annual interest. What is the
interest for the first month? What is the future value?
What is the interest for 10 years? The future value?
If we let the time, t, be a variable,
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ex. Assume you are trying to pay for tuition next semester, an estimated $4590. Your parents
agree to give you 13% simple interest on the amount of money you can give them today. How much
money would you need to give your parents in order to pay $4590 by the due date?
In general,
Def: the discount D on a discounted loan
The proceeds P of the loan is
ex. Suppose a bank offers you a $10000 discounted loan with a simple annual interest rate of 18%
over 3 years. What are your proceeds?
What is the effective interest rate?
In general,
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1.2
Compount Interest
ex. The annual interest for an account is .5%. Interest is compute every week. You deposited
$1000. What is your balance after one week? After two weeks? After one month? After 10 years?
In general,
In the example, if we let the time, t, be a variable,
What is the effective annual yield in this example?
In general,
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ex. Chase offers a savings account with a .01% nominal rate compounded monthly. Bank of America
offers a savings account with a .01% effective annual yield (APY). Which is the better account to
open?
ex. Assume you are trying to pay for tuition next semester, an estimated $4590. Your parents
agree to give you 13% nominal interest, compounded daily, on the amount of money you can give
them today. How much money would you need to give your parents in order to pay $4590 by the
due date?
In general,
1.3
Annuities and Sinking Funds
Def: an annuity is
Def: the term of an annuity is
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ex. Suppose you deposit $300 every month into a savings account with a normial rate of .5%,
compounded monthly. How much will you have in your account at the end of the year?
For b < 1, a + ab + ab2 + ... + abn−1 =
In general,
In this example, how much money is in the account at the end of 5 years?
How much interest is earned in this example?
Def:
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ex. Assume you are trying to pay for tuition next semester, an estimated $4590. Your parents
agree to give you 13% nominal interest, compounded per quarter, on your quarterly payments.
How much must your payment be in order to pay $4590 by the due date?
What if payments and interest were compounded weekly?
What is the interest gained in the fifth period?
What is the interest gained in the third week of the second month?
In general,
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