Gr 11 Math Ch 9 SUM: Finance, Growth and Decay
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Questions and Answers

What is the main difference between simple and compound depreciation?

  • The way the principal amount is calculated
  • The rate at which the asset's value decreases over time
  • The number of years the asset is used for
  • The method used to calculate the depreciation amount each year (correct)

    • What is the formula for calculating the book value using simple depreciation?

  • A = P(1 + in)
  • A = P(1 + i)^n
  • A = P(1 - in) (correct)
  • A = P(1 - i)^n

    • Which type of depreciation results in a constant depreciation amount each year?

  • Compound depreciation
  • Exponential depreciation
  • Linear depreciation
  • Simple depreciation (correct)

    • What is the purpose of finding the depreciation rate (i) in simple and compound depreciation?

    <p>To solve for the depreciation rate in the respective formulas</p> Signup and view all the answers

    How does the book value change over time in compound depreciation?

    <p>It follows an exponential decay pattern</p> Signup and view all the answers

    What is the relationship between the initial value, final value, and depreciation rate in simple decay?

    <p>Linear</p> Signup and view all the answers

    How can interest be compounded besides being compounded annually?

    <p>Monthly and quarterly</p> Signup and view all the answers

    What is the purpose of using timelines in compounding calculations?

    <p>To visualize the changes in interest rates over the term of the investment or loan</p> Signup and view all the answers

    What is the main characteristic of the total depreciation calculated using simple depreciation?

    <p>It can be calculated as P × i × n</p> Signup and view all the answers

    What happens to the interest rate when amounts are compounded more than once per annum?

    <p>It is divided by the number of compounding periods per year</p> Signup and view all the answers

    What is the formula for calculating the accumulated value in simple interest?

    <p>A = P(1 + in)</p> Signup and view all the answers

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

    <p>To adjust for changes in interest rates or additional transactions</p> Signup and view all the answers

    What is the formula for calculating the effective interest rate?

    <p>1 + i-effective = (1 + i-nominal/m)^m</p> Signup and view all the answers

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

    <p>To find the total accumulated value at the end of the investment or loan term</p> Signup and view all the answers

    What happens to the principal amount in each subsequent period?

    <p>It is adjusted for any deposits or withdrawals</p> Signup and view all the answers

    What is the formula for calculating the accumulated value in compound interest?

    <p>A = P(1 + i)^n</p> Signup and view all the answers

    What is the main difference between simple and compound depreciation in terms of the value of the asset?

    <p>The value of the asset decreases exponentially over time in compound depreciation.</p> Signup and view all the answers

    What is the effect of compounding more than once a year on the interest rate?

    <p>The interest rate increases.</p> Signup and view all the answers

    If an asset's initial value is $100,000, and it depreciates at a rate of 10% per year, what is the book value after 5 years using compound depreciation?

    <p>$59,049</p> Signup and view all the answers

    What happens to the depreciation amount in each subsequent year using compound depreciation?

    <p>It decreases.</p> Signup and view all the answers

    What is the purpose of rearranging the formula to solve for i in simple and compound depreciation?

    <p>To find the depreciation rate.</p> Signup and view all the answers

    How does the depreciation rate affect the book value in simple and compound depreciation?

    <p>A higher depreciation rate decreases the book value.</p> Signup and view all the answers

    What is the relationship between the time period and the depreciation rate in simple depreciation?

    <p>The time period is directly proportional to the depreciation rate.</p> Signup and view all the answers

    What is the purpose of adjusting the interest rate and the number of compounding periods according to the frequency of compounding?

    <p>To ensure accurate calculations of compound interest.</p> Signup and view all the answers

    When should you break down the timeline into segments and calculate each period separately?

    <p>When interest rates change or additional deposits/withdrawals are made.</p> Signup and view all the answers

    What is the formula for calculating the accumulated value at the end of each segment?

    <p>A = P(1 + i/p)^(np)</p> Signup and view all the answers

    What is the role of the number of compounding periods per year (p) in the compound interest formula?

    <p>It determines the frequency of compounding.</p> Signup and view all the answers

    What is the result of multiplying the number of years by p and dividing the interest rate by p when amounts are compounded more than once per annum?

    <p>The number of compounding periods is adjusted.</p> Signup and view all the answers

    What is the purpose of calculating the accumulated value at the end of each period?

    <p>To adjust the principal for the next period.</p> Signup and view all the answers

    What is the relationship between the nominal interest rate and the effective interest rate?

    <p>The effective interest rate is a function of the nominal interest rate and the compounding frequency.</p> Signup and view all the answers

    What is the purpose of using the formula 1 + ieffective = (1 + inominal/m)^m?

    <p>To calculate the effective interest rate from the nominal interest rate.</p> Signup and view all the answers

    If a machine depreciates from $100,000 to $64,000 in 4 years using compound depreciation, what is the annual depreciation rate?

    <p>20%</p> Signup and view all the answers

    A company uses simple depreciation to calculate the book value of a machine. If the machine's initial value is $150,000 and the annual depreciation amount is $15,000, what is the book value after 8 years?

    <p>$60,000</p> Signup and view all the answers

    Which of the following is true about simple and compound depreciation?

    <p>Simple depreciation results in a linear decay pattern, while compound depreciation results in an exponential decay pattern.</p> Signup and view all the answers

    An investment of $10,000 is compounded quarterly at a nominal annual interest rate of 8%. What is the effective interest rate per quarter?

    <p>1.5%</p> Signup and view all the answers

    What is the total depreciation of an asset that depreciates at a rate of 12% per year for 5 years using simple depreciation, if the initial value is $80,000?

    <p>$48,000</p> Signup and view all the answers

    If an asset depreciates from $200,000 to $120,000 in 3 years using compound depreciation, what is the annual depreciation rate?

    <p>15%</p> Signup and view all the answers

    Which of the following is a key characteristic of compound depreciation?

    <p>Depreciation amount changes each year, decreasing as the asset's value decreases.</p> Signup and view all the answers

    An investment of $50,000 is compounded monthly at a nominal annual interest rate of 6%. What is the frequency of compounding?

    <p>12 times per year</p> Signup and view all the answers

    What is the correct formula to find the accumulated value when interest is compounded more than once per annum?

    <p>A = P(1 + i/p)^{np}</p> Signup and view all the answers

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

    <p>To break down the periods into segments and calculate each period separately</p> Signup and view all the answers

    What happens to the principal amount when interest is compounded more than once per annum?

    <p>It is adjusted for each compounding period</p> Signup and view all the answers

    How is the nominal interest rate related to the effective interest rate?

    <p>The nominal interest rate is used to calculate the effective interest rate</p> Signup and view all the answers

    What is the purpose of calculating the accumulated value at the end of each period?

    <p>To adjust the principal amount for the next period</p> Signup and view all the answers

    How are the number of years and interest rate adjusted when amounts are compounded more than once per annum?

    <p>The number of years is multiplied by p and the interest rate is divided by p</p> Signup and view all the answers

    What is the purpose of breaking down the timeline into segments and calculating each period separately?

    <p>To account for changes in interest rates or additional transactions</p> Signup and view all the answers

    What is the role of the number of compounding periods per year (p) in the compound interest formula?

    <p>It adjusts the interest rate according to the frequency of compounding</p> Signup and view all the answers

    What is the main difference between nominal and effective interest rates in the context of compound interest?

    <p>Nominal interest rate is the rate at which interest is compounded, while effective interest rate is the rate at which the principal grows.</p> Signup and view all the answers

    When breaking down the timeline into segments for compound interest calculations, what should you do at the end of each segment?

    <p>Calculate the accumulated value and adjust the principal for the next period.</p> Signup and view all the answers

    What happens to the interest rate when amounts are compounded more than once per annum?

    <p>It is divided by the number of compounding periods per year.</p> Signup and view all the answers

    What is the effect of decreasing the depreciation rate on the book value of an asset over time, using simple depreciation?

    <p>The book value decreases at a slower rate, but the depreciation amount remains constant.</p> Signup and view all the answers

    If an asset's book value is $80,000 after 3 years of depreciation using compound depreciation, and the initial value was $100,000, what can be said about the depreciation rate?

    <p>The depreciation rate is less than 10%.</p> Signup and view all the answers

    What is the purpose of using the formula 1 + ieffective = (1 + inominal/m)^m?

    <p>To find the effective interest rate from the nominal interest rate.</p> Signup and view all the answers

    What is the role of the number of compounding periods per year (p) in the compound interest formula?

    <p>It determines the frequency of compounding.</p> Signup and view all the answers

    What is the relationship between the principal amount and the depreciation rate in compound depreciation?

    <p>The principal amount decreases as the depreciation rate increases.</p> Signup and view all the answers

    What is the result of multiplying the number of years by p and dividing the interest rate by p when amounts are compounded more than once per annum?

    <p>The frequency of compounding is adjusted.</p> Signup and view all the answers

    What happens to the total depreciation when the depreciation rate increases in simple depreciation?

    <p>The total depreciation increases, and the book value decreases at a faster rate.</p> Signup and view all the answers

    What is the purpose of calculating the accumulated value at the end of each period?

    <p>To adjust the principal for the next period.</p> Signup and view all the answers

    If an asset depreciates from $150,000 to $90,000 in 5 years using compound depreciation, what can be said about the depreciation rate?

    <p>The depreciation rate is less than 15%.</p> Signup and view all the answers

    What is the effect of increasing the time period on the book value of an asset using compound depreciation?

    <p>The book value decreases at a faster rate, and the depreciation amount also increases.</p> Signup and view all the answers

    What happens to the principal amount when interest is compounded more than once per annum?

    <p>It is adjusted for each period.</p> Signup and view all the answers

    What is the relationship between the principal amount and the time period in simple depreciation?

    <p>The principal amount decreases as the time period increases.</p> Signup and view all the answers

    What happens to the book value of an asset when the time period is reduced, using compound depreciation?

    <p>The book value decreases at a slower rate.</p> Signup and view all the answers

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