Keith makes an investment of $3000 paying at an interest rate of 7.5% per year, compounded

quarterly.

a. One form of the compound interest formula isA=P(1i)+, whereAis the amount of

money at the end of the investment;Pis the principal amount deposited;iis the interest

rate per compounding period; andnis the number of compounding periods.

Use the above formula toalgebraically determinethe number of compounding periods it would take for the investment to double. (Hint: Review page 362 in the textbook to help you set up this equation and then solve using the logarithmic laws.)Stateyour value fornto one decimal place.

b.Explain why the correct solution for the number of compounding periods is 38 and not 37.

c. Another form of the compound interest formula isA=P(1n)+, whereAis the

1. amount of money at the end of the investment;Pis the principal amount deposited;ris the interest rate per year;nis the number of compounding periods a year; andtis the total time in years.
2. Using this second formulagraphically determinethe time in years it would take for the investment to double. Show your work by completing the statements below for your graphing calculator steps.Explainhow this answerverifiesyour results from part a. (Hint: There are 3 months in each compounding period.)

y1=

y2=

t=