FORMULAS NEEDED FOR 8.2 EXERCISES
SIMPLE INTEREST
(
or
)
(
(because
)
where:
= amount of simple interest
= principal or present value
= accumulated amount or future value
= interest rate (as a decimal)
= time (in years)
COMPOUND INTEREST
(
)
- and are the same as above and
,
and is the number of compounding periods/year
Annually ->
Semiannually ->
Quarterly ->
Monthly ->
*If a problem uses daily compounding, it will always tell you how
many days to use for .
PAYMENTS ON AMORTIZED SIMPLE INTEREST LOANS
To calculate the payments on a simple interest loan:
1. Use the simple interest formula for future value
(
) to find A.
2. Calculate the total number of loan payments, n, over the
term of the loan. Assuming that you know the number of
payments/year and the number of years of the loan, this will
just be: n = (# payments/year)(# of years).
3. The payment per period (usually monthly) is .
(In words, divide the answer from step 1 by the answer from step 2.)
NOTE: Payments on compound interest loans are covered later.
Exercises. Section 8.2: Interest
Find the simple interest if:
Principal is $500, Rate of Interest is 11%, Time is 2 yrs
If the simple interest on $3000 for 9 years is $1620, then what
is the rate?
Use the future value formula for simple interest to find P if
A=$2448, r=6%, t=6.
What is the value of an account at the end of 6 years if a
principal of $13,000 is deposited in an account at an annual
interest rate of 4% compounded monthly?
(Round final answer to the nearest cent.)
A student has a government-backed loan for which payments
are not due and interest does not accumulate until the student
stops attending college. If the student borrowed $10,000 at an
annual interest rate of 7.5%, how much interest is due 4
months after the student must begin payments?
A family is planning a vacation in 2 years. They want to get a
certificate of deposit for $1500 that can be cashed in for the
trip. What is the minimum annual simple interest rate needed
to have $2100 for the vacation?
The Consumer Price
Index (CPI) is an inflation
measure and is equal to
the percent of change in
the CPI between 2 years.
a. What was the inflation rate from 1950 to 1990?
(Round inflation rate percent to one decimal place.)
b. If a pair of sneakers cost $38 in 1950, use the CPI to
estimate the cost in 1990. (Use the unrounded
value from part a but round the final answer to the
nearest cent.)
Compute the monthly payment for a simple interest loan of
$2660, with an annual interest rate of 8% and a term of 5 years.
(Round answer to the nearest cent)
A student graduates from college with $43,000 in student loans
and a 6.5% annual simple interest rate. To reduce his debt as
quickly as possible, beginning next month he is going to pay
$700 per month toward the loan. After his first payment, how
much will he still owe on the loan? (Round answer to nearest
cent)