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

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?

To solve for the depreciation rate in the respective formulas Signup and view all the answers

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

It follows an exponential decay pattern Signup and view all the answers

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

Linear Signup and view all the answers

How can interest be compounded besides being compounded annually?

Monthly and quarterly Signup and view all the answers

What is the purpose of using timelines in compounding calculations?

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

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

It can be calculated as P × i × n Signup and view all the answers

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

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

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

A = P(1 + in) Signup and view all the answers

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

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

What is the formula for calculating the effective interest rate?

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

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

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

What happens to the principal amount in each subsequent period?

It is adjusted for any deposits or withdrawals Signup and view all the answers

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

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

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

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

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

The interest rate increases. 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?

$59,049 Signup and view all the answers

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

It decreases. Signup and view all the answers

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

To find the depreciation rate. Signup and view all the answers

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

A higher depreciation rate decreases the book value. Signup and view all the answers

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

The time period is directly proportional to the depreciation rate. 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?

To ensure accurate calculations of compound interest. Signup and view all the answers

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

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

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

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

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

It determines the frequency of compounding. 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?

The number of compounding periods is adjusted. Signup and view all the answers

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

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

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

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

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

To calculate the effective interest rate from the nominal interest rate. 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?

20% 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?

$60,000 Signup and view all the answers

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

Simple depreciation results in a linear decay pattern, while compound depreciation results in an exponential decay pattern. 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?

1.5% 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?

$48,000 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?

15% Signup and view all the answers

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

Depreciation amount changes each year, decreasing as the asset's value decreases. 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?

12 times per year 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?

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

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

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

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

It is adjusted for each compounding period Signup and view all the answers

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

The nominal interest rate is used to calculate the effective interest rate Signup and view all the answers

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

To adjust the principal amount for the next period 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?

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

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

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

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

It adjusts the interest rate according to the frequency of compounding Signup and view all the answers

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

Nominal interest rate is the rate at which interest is compounded, while effective interest rate is the rate at which the principal grows. 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?

Calculate the accumulated value and adjust the principal for the next period. Signup and view all the answers

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

It is divided by the number of compounding periods per year. 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?

The book value decreases at a slower rate, but the depreciation amount remains constant. 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?

The depreciation rate is less than 10%. Signup and view all the answers

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

To find the effective interest rate from the nominal interest rate. Signup and view all the answers

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

It determines the frequency of compounding. Signup and view all the answers

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

The principal amount decreases as the depreciation rate increases. 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?

The frequency of compounding is adjusted. Signup and view all the answers

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

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

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

To adjust the principal for the next period. 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?

The depreciation rate is less than 15%. 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?

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

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

It is adjusted for each period. Signup and view all the answers

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

The principal amount decreases as the time period increases. Signup and view all the answers

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

The book value decreases at a slower rate. Signup and view all the answers

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

Questions and Answers

What is the main difference between simple and compound depreciation?

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

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

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

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

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

How can interest be compounded besides being compounded annually?

What is the purpose of using timelines in compounding calculations?

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

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

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

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

What is the formula for calculating the effective interest rate?

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

What happens to the principal amount in each subsequent period?

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

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

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

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?

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

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

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

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

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

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

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

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

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?

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

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

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

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

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?

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

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

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?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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?

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

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

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

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?

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

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

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

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

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

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

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

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Gr 11 Math Ch 9: Simple and Compound Depresiation