Gr12 Mathematics: Ch 3.1 Calculating the Period of an Investment

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What is the main difference between simple interest and compound interest?

Simple interest is calculated on the principal amount, while compound interest is calculated on the principal plus interest. (correct)

Simple interest is calculated on the principal amount, while compound interest is calculated on the principal minus interest.

Simple interest is always higher than compound interest.

Simple interest is calculated for a shorter period, while compound interest is calculated for a longer period.

What is the formula to calculate the accumulated amount in compound interest?

A = P(1 - in)

A = P(1 + in)

A = P(1 - i)^n

A = P(1 + i)^n (correct)

What is the purpose of using logarithms when solving for the time period in compound interest calculations?

To calculate the principal amount

To calculate the interest rate

To calculate the accumulated amount

To simplify the calculation of the time period (correct)

What does the nominal interest rate reflect?

The stated interest rate Signup and view all the answers

What is the formula to solve for the time period (n) in compound interest calculations?

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

What is the main difference between simple depreciation and compound depreciation?

Simple depreciation assumes a linear reduction in value, while compound depreciation considers the reduced value in each period Signup and view all the answers

What is the formula to calculate the value after depreciation using simple depreciation?

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

What is the relationship between the effective annual interest rate (i) and the nominal interest rate (i(m))?

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

What is the main purpose of using logarithms in compound interest calculations?

To solve for the time period Signup and view all the answers

If a principal amount of $100 is invested at a 5% annual compound interest rate, what will be the accumulated amount after 2 years?

$110.25 Signup and view all the answers

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

The effective annual interest rate is the nominal interest rate compounded m times per year Signup and view all the answers

What is the main difference between the formulas for simple and compound interest?

The exponent in the formula Signup and view all the answers

If a machine depreciates at a rate of 10% per year, what will be its value after 3 years if its initial value is $10,000?

$6,561.00 Signup and view all the answers

What is the formula to calculate the value after depreciation using compound depreciation?

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

If an investment triples in value over 5 years, what can be said about the interest rate?

The interest rate is 14.42% per year Signup and view all the answers

What is the main purpose of using the nominal interest rate?

To reflect the stated interest rate Signup and view all the answers

A company invests $50,000 at an annual compound interest rate of 8%. How many years will it take for the investment to double?

7 years Signup and view all the answers

A car's value depreciates at a rate of 15% per year. If its initial value is $20,000, what will be its value after 4 years?

$9,100 Signup and view all the answers

A bank offers a nominal interest rate of 12% compounded quarterly. What is the effective annual interest rate?

12.55% Signup and view all the answers

If the accumulated amount of an investment is $75,000 and the principal amount is $50,000, what is the interest rate per period if the investment is compounded annually for 5 years?

12% Signup and view all the answers

A machine depreciates at a rate of 20% per year. If its initial value is $15,000, what will be its value after 2 years using the simple depreciation method?

$9,000 Signup and view all the answers

If the effective annual interest rate is 9.5%, what is the nominal interest rate compounded semiannually?

9.25% Signup and view all the answers

A company invests $25,000 at an annual compound interest rate of 10%. How many years will it take for the investment to grow by 50%?

4 years Signup and view all the answers

If the value of a machine is $12,000 after 3 years and it depreciates at a constant rate, what was its initial value if the depreciation rate is 10% per year using the compound depreciation method?

$20,000 Signup and view all the answers