1. Warmup 5-12 1. Find the inverse: 2. Find the inverse:
3. Condense the following log expression with one log:
4. Expand the following log into multiple logs:
Solve for x:

2. Notes – Compound Interest Formula and Pert With Logs
Remember , the formula for compound interest is:
A = P(1 + (r/n))(n*t) with A = Amount earned,
P = Principle(amount Put in)
r = interest rate
n = number of times interest is
compounded in a year
t = time in years
Steps to find t with logs:
Plug in all values given for A, P, n and r into formula.
Divide both sides by P.
Use calculator to evaluate the (1 + (r/n)) part of formula.(DO NOT
ROUND OFF)
Put log with the base found in step 3 on both sides of = in front of
each side. This will cancel out the base found in step 3. Exponent
can then be brought down.
5. Use the calculator and change of base to calculate answer to left
side of =.(Round to 2 decimal places)
Set exponent(n*t) = to amount obtained in step 5 and divide both
sides by number in front of t. (Round to 2 decimal places)
Ex. Jeremy has $2500 to invest in an account that earns 6% interest,
compounded monthly. How many years will it take him to make
$4000?
Ex. Joan has $4800 to invest in an account that earns 4.5% interest,
compounded quarterly. How many years will it take her to earn
$7200?
Ex. Tim has $3500 to invest in an account compounded monthly for 6 years.
What interest rate would he need to have $4900 at the end of the 6 years?
Ex. Terri has $8400 to invest in an account that is compounded quarterly for
8 years. What interest rate would she need in order to double her money at
the end of the 8 years?

3. 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?

4. 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.
1. Dave has $2400 to invest in an account earning 5% interest,
compounded monthly. How many years would he need to invest
the money in order to make a total of $4200?
2. Doris has $6400 to invest in an account earning 4.5% interest,
compounded quarterly. How many years would she need to
invest the money in order to make a total of $8960?
3. . Chris has $5900 to invest in an account earning 6.5% interest,
compounded weekly. How many years would he need to invest
the money in order to double his money?

5. 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.
4. Christine has $3600 to invest in an account compounded
monthly for 4 years. What interest rate does she need to get
$6480 at the end of the 4 years?
5. Keith has $4800 to invest in an account compounded
quarterly for 7 years. What interest rate does he need to get $8000
at the end of the 7 years?
6. Marie has $7600 to invest in an account compounded daily for
5 years. What interest rate would she need to double her money at
the end of the 5 years?

6. 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?

7. 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?

8. Ticket out the door 5-12 Compound Interest with Logs
Solve the following problems for r or t. Show work! Round all answers
to 2 decimal places.
1. Terri has $4500 to invest in an account compounded
monthly for 5 years. What interest rate does she need to get
$6300 at the end of the 5 years?
2. Adam has $9600 to invest in an account earning 5.25% interest compounded
quarterly. How long would he need to invest the money to earn $12000 at the end
the investment?
3. Ellen has $15800 to invest in an account compounded
continuously for 4 years. What interest rate would she need to
make $18960 at the end of the 4 years?
4. Brett has $7500 to invest in an account earning 4.75% interest compounded
continuously. How long would he need to invest his money to have double his
original investment at the end of the term?

9. Warmup 12-4 1. Find the inverse: 2. Find the inverse:
3. Condense the following log expression with one log:
4. Condense the following log expression with one log:
Solve for x: