MATH 110 Sec 8-2: Interest
Practice Exercises
Find the simple interest if the
principal is $500, the interest rate is 11%
and the time is 2 years.
MATH 110 Sec 8-2: Interest
Practice Exercises
Find the simple interest if the
principal is $500, the interest rate is 11%
and the time is 2 years.
𝐼 = 𝑃𝑟𝑡
MATH 110 Sec 8-2: Interest
Practice Exercises
If the simple interest on $3000 for
9 years is $1620, then what is the rate?
MATH 110 Sec 8-2: Interest
Practice Exercises
If the simple interest on $3000 for
9 years is $1620, then what is the rate?
𝐼 = 𝑃𝑟𝑡
MATH 110 Sec 8-2: Interest
Practice Exercises
Use the future value formula for simple
interest to find P if A=$2448, r=6%, t=6.
MATH 110 Sec 8-2: Interest
Practice Exercises
Use the future value formula for simple
interest to find P if A=$2448, r=6%, t=6.
𝐴 = 𝑃(1 + 𝑟𝑡)
MATH 110 Sec 8-2: Interest
Practice Exercises
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.)
MATH 110 Sec 8-2: Interest
Practice Exercises
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.)
𝑟
𝑛
𝐴 = 𝑃(1 + 𝑖) where 𝑖 = , 𝑛 = 𝑚𝑡
𝑚
MATH 110 Sec 8-2: Interest
Practice Exercises
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.)
𝑟
𝑛
𝐴 = 𝑃(1 + 𝑖) where 𝑖 = , 𝑛 = 𝑚𝑡
𝑚
Also remember that:
A = accumulated (future) value
P = principal (present value)
t = time (in years)
r = annual interest rate (decimal)
MATH 110 Sec 8-2: Interest
Practice Exercises
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?
MATH 110 Sec 8-2: Interest
Practice Exercises
A family is planning a vacation in 2 years. They want
to get a certificate of deposit for $1500 to be cashed in
for the trip. What is the minimum annual simple
interest rate needed to have $2100 for the vacation?
MATH 110 Sec 8-2: Interest
Practice Exercises
A family is planning a vacation in 2 years. They want
to get a certificate of deposit for $1500 to be cashed in
for the trip. What is the minimum annual simple
interest rate needed to have $2100 for the vacation?
Solution I:
𝐼 = 𝑃𝑟𝑡
MATH 110 Sec 8-2: Interest
Practice Exercises
A family is planning a vacation in 2 years. They want
to get a certificate of deposit for $1500 to be cashed in
for the trip. What is the minimum annual simple
interest rate needed to have $2100 for the vacation?
Solution I:
𝐼 = 𝑃𝑟𝑡
Answer:
𝑟 = 20%
Solution II:
𝐴 = 𝑃(1 + 𝑟𝑡)
MATH 110 Sec 8-2: Interest
Practice Exercises
The Consumer Price Index (CPI) is an inflation
measure and is equal to the percent of change in
the CPI between 2 years.
MATH 110 Sec 8-2: Interest
Practice Exercises
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.)
MATH 110 Sec 8-2: Interest
Practice Exercises
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.)
Note: The inflation rate (using CPI) is a percent change:
𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑅𝑎𝑡𝑒 =
𝑁𝑒𝑤 𝐶𝑃𝐼 − 𝑂𝑙𝑑 𝐶𝑃𝐼 1990 𝐶𝑃𝐼 − 1950 𝐶𝑃𝐼
=
𝑂𝑙𝑑 𝐶𝑃𝐼
1950 𝐶𝑃𝐼
MATH 110 Sec 8-2: Interest
Practice Exercises
The Consumer Price Index (CPI) is an inflation
measure and is equal to the percent of change in
the CPI between 2 years.
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.)
MATH 110 Sec 8-2: Interest
Practice Exercises
The Consumer Price Index (CPI) is an inflation
measure and is equal to the percent of change in
the CPI between 2 years.
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.)
Note 1: The unrounded value from part a was: 𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑅𝑎𝑡𝑒 = 4.759358 = 475.9358%.
MATH 110 Sec 8-2: Interest
Practice Exercises
The Consumer Price Index (CPI) is an inflation
measure and is equal to the percent of change in
the CPI between 2 years.
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.)
Note 1: The unrounded value from part a was: 𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑅𝑎𝑡𝑒 = 4.759358 = 475.9358%.
Note 2: The percent change in price from 1950 to 1990 is just the inflation rate from part a.
MATH 110 Sec 8-2: Interest
Practice Exercises
The Consumer Price Index (CPI) is an inflation
measure and is equal to the percent of change in
the CPI between 2 years.
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.)
Note 1: The unrounded value from part a was: 𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑅𝑎𝑡𝑒 = 4.759358 = 475.9358%.
Note 2: The percent change in price from 1950 to 1990 is just the inflation rate from part a.
𝐸𝑠𝑡. 𝑐𝑜𝑠𝑡 𝑖𝑛 1990 − 𝐶𝑜𝑠𝑡 𝑖𝑛 1950
= 𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝑓𝑟𝑜𝑚 𝑝𝑎𝑟𝑡 𝑎
𝐶𝑜𝑠𝑡 𝑖𝑛 1950
MATH 110 Sec 8-2: Interest
Practice Exercises
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.)
MATH 110 Sec 8-2: Interest
Practice Exercises
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.)
Strategy:
Step 1: Find the future value A of the loan.
MATH 110 Sec 8-2: Interest
Practice Exercises
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.)
Strategy:
Step 1: Find the future value A of the loan.
Step 2: Divide A by the total number of payments
for the life of the loan
MATH 110 Sec 8-2: Interest
Practice Exercises
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.)
Strategy:
Step 1: Find the future value A of the loan.
MATH 110 Sec 8-2: Interest
Practice Exercises
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.)
Strategy:
Step 1: Find the future value A of the loan. A = $3724
Step 2: Divide A by the total number of payments
for the life of the loan
MATH 110 Sec 8-2: Interest
Practice Exercises
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.)
Strategy:
Step 1: Find the future value A of the loan. A = $3724
Step 2: Divide A by the total number of payments
for the life of the loan where
# of payments = (12 / year)(5 years) = 60
MATH 110 Sec 8-2: Interest
Practice Exercises
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.)
MATH 110 Sec 8-2: Interest
Practice Exercises
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.)
Strategy
Step 1: Find amt of interest owed for 1st month.
MATH 110 Sec 8-2: Interest
Practice Exercises
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.)
Strategy
Step 1: Find amt of interest owed for 1st month.
Step 2: Find total owed (Principal + Interest).
MATH 110 Sec 8-2: Interest
Practice Exercises
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.)
Strategy
Step 1: Find amt of interest owed for 1st month.
Step 2: Find total owed (Principal + Interest).
Step 3: Subtract off the 1st month’s actual payment.
MATH 110 Sec 8-2: Interest
Practice Exercises
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.)
Strategy
Step 1: Find amt of interest owed for 1st month.
MATH 110 Sec 8-2: Interest
Practice Exercises
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.)
Strategy
Step 1: Find amt of interest owed for 1st month.
𝐼 = 𝑃𝑟𝑡
MATH 110 Sec 8-2: Interest
Practice Exercises
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.)
Strategy
Step 1: Find amt of interest owed for 1st month.
𝐼 = 𝑃𝑟𝑡
1
Note: Time (t) must be in years and 𝑡 = 12 year.
MATH 110 Sec 8-2: Interest
Practice Exercises
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.)
Strategy
Step 1: Find amt of interest owed for 1st month. $232.92
MATH 110 Sec 8-2: Interest
Practice Exercises
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.)
Strategy
Step 1: Find amt of interest owed for 1st month. $232.92
Step 2: Find total owed (Principal + Interest).
TOTAL OWED = PRINCIPAL + INTEREST
MATH 110 Sec 8-2: Interest
Practice Exercises
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.)
Strategy
Step 1: Find amt of interest owed for 1st month. $232.92
Step 2: Find total owed (Principal + Interest). $43232.92
MATH 110 Sec 8-2: Interest
Practice Exercises
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.)
Strategy
Step 1: Find amt of interest owed for 1st month. $232.92
Step 2: Find total owed (Principal + Interest). $43232.92
Step 3: Subtract off the 1st month’s actual payment ($700).
$43232.92 - $700.00 = $42532.92