Notes – Compound Interest Formula and Pe rt With Logs Remember, the formula for compound interest is: A = P(1 + (r/n)) (n*t) with A = Amount earned, P.

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Notes – Compound Interest Formula and Pe rt 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: 1.Plug in all values given for A, P, n and r into formula. 2.Divide both sides by P. 3.Use calculator to evaluate the (1 + (r/n)) part of formula.(DO NOT ROUND OFF) 4.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) 6.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 that earns 5% interest, compounded quarterly. How many years will it take him to double his money?

Notes – Compound Interest Formula and Pe rt 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: 1.Plug in all values given for A, P, and r OR t into formula. 2.Divide both sides by P.(round to 2 decimal places) 3.Place ln on both sides of = in front of each side. ln and e will cancel out and exponent will come down. 4.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?

Compound Interest Formula and Pe rt 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?

Compound Interest Formula and Pe rt 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 monthly for 5 years. What interest rate would she need to double her money at the end of the 5 years?

Compound Interest Formula and Pe rt 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, compounded continuously. How many years would she need to invest the money in order to double her money?

Compound Interest Formula and Pe rt 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? 12.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?

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: 5.Solve for x: 6.Solve for x: 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: 5.Solve for x: 6.Solve for x: Warmup 12-4