1. Notes – Compound Interest Formula and Pert With Logs
Remember , the formula for continuously compounded interest is:
A = Pe(r*t) with A = Amount earned,
P = Principle(amount Put in)
r = interest rate
t = time in years
Steps to find r or t:
Plug in all values given for A, P, and r OR t into formula.
Divide both sides by P.(round to 2 decimal places)
Place ln on both sides of = in front of each side. ln and e will
cancel out and exponent will come down.
Use calculator to find the ln of the number on the left side of the =.
5. Set exponent = to number obtained in step 4 and divide by the
number next to r or t on both sides.
Ex. Robert has $4200 to invest in an account earning 4% interest,
compounded continuously. How many years would he need to invest
the money in order to make a total of $5600?
Ex. Jane has $6250 to invest in an account earning 5.5% interest,
compounded continuously. How many years would she need to
invest the money in order to make a total of $10000?
Ex. Michael has $8400 to invest in an account compounded
continuously for 6 years. What interest rate does he need to get
$12600 at the end of the 6 years?
Ex. Michelle has $4700 to invest in an account compounded
continuously for 8 years. What interest rate does she need to double
her money at the end of the 8 years?

2. Compound Interest Formula and Pert With Logs Practice
Solve the following problems for r or t. Show work! Round all answers
to 2 decimal places.
7. Delores has $9600 to invest in an account earning 5.5% interest,
compounded continuously. How many years would she need to invest
the money in order to make a total of $14400?
8. Jeff has $7500 to invest in an account earning 4.5% interest,
compounded continuously. How many years would he need to
invest the money in order to make a total of $13500?
9. Francis has $8700 to invest in an account earning 6% interest,
the money in order to double her money?

3. Compound Interest Formula and Pert With Logs Practice
Solve the following problems for r or t. Show work! Round all answers
to 2 decimal places.
10. Tracy has $2700 to invest in an account compounded
continuously for 6 years. What interest rate does she need to get
$4500 at the end of the 6 years?
11. Allen has $13200 to invest in an account compounded
continuously for 8 years. What interest rate does he need to get $21120
at the end of the 8 years?
Marion has $13900 to invest in an account compounded
continuously for 7years. What interest rate would she need to
double her money at the end of the 7 years?

4. Warmup 12-7 Solve the following equations for x. Show work!
Round to 2 decimal places. 1. 2.
3. Condense the following log expression:
4. Expand the following log expression:
5. Find the inverse:
6. Mark has $10800 to invest at 6% interest compounded quarterly. How long would he need to
invest the money to earn a total of $14040?

5. Warmup 12-7 Solve the following equations for x. Show work!
Round to 2 decimal places. 1. 2.
3. Condense the following log expression:
4. Expand the following log expression:
5. Find the inverse:
6. Mary has $12000 to invest at 4.75% interest compounded quarterly. How long would she need to
invest the money to earn a total of $14400?

6. Notes –Depreciation Formulas
Depreciation Formula: A = P(1 – r)t where A = Amount item is
worth
P = original value
of item
r = rate of decrease
(converted to a
decimal)
t = time in years
Ex. If a person paid $32000 for a new car, and the
car’s value depreciates at a rate of 15% per year, how many years
before the car is worth:
a. $25000? b. $18000? c. $10000
d. $5000?
Ex. If a person paid $1450 for a new computer, and the
computer’s value depreciates at a rate of 28% per year, how many
years until the computer is worth:
a. $1000? b. $725? c. $400?
d. $100?
Ex. If a person paid $300 for a cell phone, and the phone’s
value depreciates at a rate of 12% per year, how many years
until the phone is worth:
a. $200? b. $150? c. $50?

7. Depreciation Practice
1. A person bought a car for $ The car’s value goes down
16% per year. How many years until the car is worth:
a. $25000? b. $17500?
c. $10000? d. $5000?
2. A person bought a computer for $875. The computer’s
value goes down 26% per year. How many years until the computer
is only worth:
$600? b. $438?
$250? d. $100?
3. A person bought a plasma HDTV for $ The value of the TV goes down 24% per
year. How many years will it take for the TV to be worth only:
$1000? b. $750?
c. $450? d $150?
4. A person bought a smart phone for $500. The phone’s
value goes down 19% per year. How many years until the phone
Is only worth:
a. $400? b. $250?
c. $100? d. $50?