Understanding Compound Interest

The video tutorial explains how to calculate the time required for an investment to grow from $1,000 to $1,500 with a 3% annual interest rate compounded monthly. It covers the calculation of monthly interest, the use of logarithms to solve for the number of months, and the conversion of months to years. The tutorial concludes that it will take approximately 14 years for the investment to reach the target amount.

What is the initial amount Carolyn invested?

• $1,000

• $1,500

• $11,000

• $15,000

How is the monthly interest rate calculated from the annual rate?

• Divide by 6

• Multiply by 12

• Divide by 12

• Add 3%

What is the monthly interest rate as a percentage?

• 0.5%

• 1%

• 3%

• 0.25%

What is the equation used to find the number of months needed for the investment to grow?

• 1.0025^N = 2

• 1.025^N = 1.5

• 1.03^N = 1.5

• 1.0025^N = 1.5

Which mathematical operation is used to solve for N in the equation?

• Addition

• Subtraction

• Logarithm

• Multiplication

What is the base of the logarithm used in the calculation?

• Base e

• Base 5

• Base 10

• Base 2

How many months does it take for the investment to reach $1,500?

• 120 months

• 14 months

• 133 months

• 162 months

How many years does it take for the investment to reach $1,500 when rounded to the nearest whole year?

• 15 years

• 14 years

• 13 years

• 12 years

What is the final amount Carolyn wants her investment to grow to?

• $15,000

• $11,000

• $1,500

• $1,000

What is the significance of the number 1.0025 in the context of this problem?

• It is the annual interest rate

• It is the monthly interest rate

• It is the growth factor per month

• It is the total amount after one year