Gr 11 Math Ch 9: Timelines

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What is the purpose of using timelines in compounding interest calculations?

To calculate the accumulated value at the end of each period

To visualize the periods and changes in compounding and interest rates over the term of the investment or loan (correct)

To adjust the principal for deposits or withdrawals

To determine the annual interest rate

When interest rates change or additional deposits/withdrawals are made, how should the timeline be handled?

Stop the calculation and restart with the new interest rate

Break the timeline into segments and calculate each period separately (correct)

Average the interest rates and calculate the accumulated value for the entire term

Ignore the changes and calculate the accumulated value for the entire term

What is the formula to calculate the accumulated value in compounding interest?

A = P(1 + i)^n

A = P(1 + i-np)

A = P(1 - i/p)^(np)

A = P(1 + i/p)^(np) (correct)

What should be done to the principal after the initial period in compounding interest calculations?

Adjust the principal for any deposits or withdrawals Signup and view all the answers

Why is it necessary to modify the interest rate when compounding more than once a year?

To accurately reflect the compounding periods per year Signup and view all the answers

What is the purpose of calculating the accumulated value for each period in compounding interest?

To calculate the total accumulated value at the end of the investment or loan term Signup and view all the answers

What is the term for the number of times interest is compounded per year?

Number of compounding periods per year Signup and view all the answers

When is it necessary to recalculate the accumulated value in compounding interest?

All of the above Signup and view all the answers

What happens to the number of years when compounding more than once a year?

It is multiplied by p Signup and view all the answers

What is the effect of increasing the number of compounding periods on the accumulated value?

It increases the accumulated value Signup and view all the answers

What is the purpose of breaking down the timeline into segments?

To calculate the accumulated value at the end of each segment Signup and view all the answers

What happens to the principal amount after the initial period?

It is increased by the interest earned Signup and view all the answers

What is the effect of decreasing the number of compounding periods on the accumulated value?

It decreases the accumulated value Signup and view all the answers

Why is it necessary to adjust the interest rate when compounding more than once a year?

To account for the increased compounding frequency Signup and view all the answers

What is the result of summing the values from each period?

The total accumulated value Signup and view all the answers

What is the purpose of calculating the accumulated value for each segment?

To adjust the principal for the next period Signup and view all the answers

What is the effect on the accumulated value when the number of compounding periods per year increases, while keeping the annual interest rate constant?

The accumulated value increases Signup and view all the answers

If an investment has an annual interest rate of 5% and is compounded quarterly, what is the effective interest rate per compounding period?

1.25% Signup and view all the answers

What is the purpose of recalculating the accumulated value for each subsequent period?

To account for changes in the interest rate or compounding frequency Signup and view all the answers

What happens to the number of years in the compound interest formula when compounding more than once a year?

It increases by a factor of p Signup and view all the answers

Why is it necessary to adjust the principal amount after the initial period?

To account for the interest earned in the initial period Signup and view all the answers

What is the result of compounding interest more than once a year, when the annual interest rate remains constant?

The accumulated value increases Signup and view all the answers

What is the purpose of using a timeline in compounding interest calculations?

To visualize the periods and changes in compounding and interest rates Signup and view all the answers

When does the effective interest rate per compounding period become equal to the annual interest rate?

When compounding annually Signup and view all the answers