Question 1

What simple interest rate per year will give same future value at the end of 3 years as 10% p.a.compounded semi- annually?

Accepted Answer

Let P be the principal amount

Future Value after 3 years when interest is compounded semi-annually at 10% p.a. = P(1 + 0.05)^6

Let the Simple Interest Rate be x% per year

Future Value after 3 years when interest is compounded annually at x% p.a. = P(1 + 0.01x)^3

According to the question, the two Future Values are equal. Therefore,

P(1 + 0.05)^6 = P(1 + 0.01x)^3

(1 + 0.05)^6 = (1 + 0.01x)^3

1.3401 = 1.0001x^3

x^3 = 1.3401/1.0001 = 1.3399

x = 1.3399^(1/3) - 1 = 0.1133 or 11.33% approximately.

Therefore, the best choice is (B) 11.33%.

Question 2

What is the future value of a $1,000 invested for 20 years at an interest rate of 10% p.a.compounded quarterly?

Accepted Answer

The future value of an investment is calculated using the formula FV = P(1 + r/n)^(nt), where P is the principal amount ($1,000), r is the annual interest rate (10% or 0.10), n is the number of times the interest is compounded per year (quarterly compounding means n=4), and t is the time the money is invested for in years (20 years). Plugging in the values, FV = $1,000(1 + 0.10/4)^(4*20) = $1,000(1.025)^80 ≈ $7209.57.

Question 3

What is the present value of the following set of cash flows when the discount rate is 12% p.a.compounded monthly?

Accepted Answer

A

Question 4

What is the present value of a perpetuity consisting of payments of $500 with an interest rate of 10% p.a.?

Accepted Answer

The present value of a perpetuity is calculated using the formula PV = P / r, where P is the payment amount and r is the interest rate. Here, P = $500 and r = 10% or 0.10, so PV = $500 / 0.10 = $5,000.00.

Question 5

What is the present value of an annuity consisting of 5 annual payments of $200 with an interest rate of 8% p.a.compounded annually and the first payment made immediately?

Accepted Answer

The present value of an annuity with immediate payments (annuity due) can be calculated using the formula: $PV = P \times \left(\frac{1 - (1 + r)^{-n}}{r}\right) \times (1 + r)$, where $P$ is the payment amount, $r$ is the interest rate per period, and $n$ is the number of periods. Here, $P = 200$, $r = 0.08$, and $n = 5$. Plugging these values in gives $PV = 200 \times \left(\frac{1 - (1 + 0.08)^{-5}}{0.08}\right) \times (1 + 0.08) = 200 \times 4.31213 \times 1.08 = 862.43$.

Question 6

The future value in 10 years of $1,000 invested at a 10% p.a.compounded annually interest rate will be _____________ the future value in 10 years of $1,000 invested at a 10% p.a.simple interest rate.

Accepted Answer

Compound interest will result in a higher future value than simple interest because the interest earned each year is added to the principal, resulting in a larger base for future interest calculations. Therefore, the future value of $1,000 invested at a 10% p.a.compounded annually interest rate will be greater than the future value of $1,000 invested at a 10% p.a.simple interest rate.

Question 7

At the end of a 5- year period,the difference between the future value of $200 invested at 8% p.a.simple interest and $200 invested at 8% p.a.compounded annually interest will be _______________

Accepted Answer

The answer of At the end of a 5- year...

Question 8

Which of the following statements is true?

Accepted Answer

Simple interest only pays interest on the principal amount, while compound interest pays interest on both the principal and previously accumulated interest.

Question 9

What is X in the formula X = PV(1 + r)?

Accepted Answer

The formula X = PV(1 + r) calculates the future value of a single cash flow (PV) in one period's time, taking into account the interest rate (r).

Question 10

What is the future value of $2,500 invested for 3 years at an interest rate of 11% p.a.compounded semi- annually?

Accepted Answer

The answer of What is the future value of $2,500...

Question 11

Asset A provides a cash flow of $100 in six years' time.Asset B provides a cash flow of $100 in four years' time.Which asset would a rational investor rather own?

Accepted Answer

A rational investor would prefer Asset B because it provides the same cash flow as Asset A but in a shorter time frame. This means that the investor would have access to their return faster, and potentially have the opportunity to invest the proceeds in another opportunity. Additionally, there is less uncertainty around the longer-term cash flow of Asset A, which may impact the present value of that cash flow. Therefore, Asset B is the better choice.

Question 12

Which of the following will yield the highest future value at the end of 5 years?

Accepted Answer

The answer of Which of the following will yield the...

Question 13

What is the future value of $500 invested for 4 years at a simple interest rate of 5% p.a.?

Accepted Answer

The future value of a simple interest investment can be calculated by the formula: FV = P(1+r*t), where P is the principal amount, r is the interest rate and t is the time period. 
Here, P = $500, r = 5% and t = 4 years. 
So, FV = 500(1+0.05*4) = $600. 
Therefore, the correct answer is D, $600.

Question 14

What is the future value of $3,400 invested for 7 years at a simple interest rate of 7.5% p.a.?

Accepted Answer

Future value = Principal x (1 + (simple interest rate x time))
Future value = 3400 x (1 + (0.075 x 7))
Future value = 3400 x (1 + 0.525)
Future value = 3400 x 1.525
Future value = $5,185.00

Question 15

What does the equation, (1 + r/m)^m- 1,calculate?

Accepted Answer

The answer of What does the equation, (1 + r/m)<sup>m...

Question 16

What is the present value of an annuity due consisting of 5 annual payments of $1,000 with an interest rate of 8% p.a. ,with the first payment occurring in 5 years' time?

Accepted Answer

The present value of an annuity due is calculated by first finding the present value of an ordinary annuity and then adjusting for the fact that payments are made at the beginning of each period. Since the first payment occurs in 5 years, we calculate the present value of the annuity as if it starts in 5 years and then discount it back to the present.

Question 17

What is the future value of $20 invested for 80 years at an annually compounded interest rate of 7% p.a.?

Accepted Answer

The future value of an investment can be calculated using the formula:FV = PV * (1 + r)^nwhere:PV is the present value of the investmentr is the annual interest raten is the number of yearsIn this case, we have:PV = $20r = 7% = 0.07n = 80Substituting these values into the formula, we get:FV = $20 * (1 + 0.07)^80FV = $20 * 224.234FV = $4,484.68Therefore, the future value of $20 invested for 80 years at an annually compounded interest rate of 7% p.a. is $4,484.68.

Question 18

What is the value of a share which is expected to pay a dividend of $0.11 every six months forever,on the basis that you intend to hold the shares forever,and the Australian ten- year bond rate today is 7.29%?

Accepted Answer

The value of the perpetuity can be calculated as follows:
PV = annual dividend amount / required rate of return
PV = 0.11 / (0.0729 / 2)
PV = 0.11 / 0.03645
PV = $3.02

So the value of the share is $3.02. Therefore, the best choice is B as it is the closest answer.

Question 19

What is the present value of $1,800 to be received in 1 year when the discount rate is 9.5% p.a.?

Accepted Answer

Using the formula for present value: PV = FV/(1+r)^n
Where PV is the present value, FV is the future value, r is the discount rate, and n is the number of periods.
We have PV = 1,800/(1+0.095)^1
PV = $1,643.84 (rounded to the nearest cent)
Therefore, the best choice is A.

Question 20

Which of these answers best describes an ordinary annuity?

Accepted Answer

An ordinary annuity is a series of equally sized regularly occurring cash flows extending n periods into the future, with the cash flows occurring at the end of each period. This means that the payments are made at the end of each period, rather than at the beginning, and they are of equal size.

Quiz 2: A Review of Financial Mathematics

What simple interest rate per year will give same future value at the end of 3 years as 10% p.a.compounded semi- annually?

What is the future value of a $1,000 invested for 20 years at an interest rate of 10% p.a.compounded quarterly?

What is the present value of the following set of cash flows when the discount rate is 12% p.a.compounded monthly?

What is the present value of a perpetuity consisting of payments of $500 with an interest rate of 10% p.a.?

What is the present value of an annuity consisting of 5 annual payments of $200 with an interest rate of 8% p.a.compounded annually and the first payment made immediately?

The future value in 10 years of $1,000 invested at a 10% p.a.compounded annually interest rate will be _____________ the future value in 10 years of $1,000 invested at a 10% p.a.simple interest rate.

At the end of a 5- year period,the difference between the future value of $200 invested at 8% p.a.simple interest and $200 invested at 8% p.a.compounded annually interest will be _______________

Which of the following statements is true?

What is X in the formula X = PV(1 + r) ?

What is the future value of $2,500 invested for 3 years at an interest rate of 11% p.a.compounded semi- annually?

Asset A provides a cash flow of $100 in six years' time.Asset B provides a cash flow of $100 in four years' time.Which asset would a rational investor rather own?

Which of the following will yield the highest future value at the end of 5 years?

What is the future value of $500 invested for 4 years at a simple interest rate of 5% p.a.?

What is the future value of $3,400 invested for 7 years at a simple interest rate of 7.5% p.a.?

What does the equation, (1 + r/m) ^m- 1,calculate?

What is the present value of an annuity due consisting of 5 annual payments of $1,000 with an interest rate of 8% p.a. ,with the first payment occurring in 5 years' time?

What is the future value of $20 invested for 80 years at an annually compounded interest rate of 7% p.a.?

What is the value of a share which is expected to pay a dividend of $0.11 every six months forever,on the basis that you intend to hold the shares forever,and the Australian ten- year bond rate today is 7.29%?

What is the present value of $1,800 to be received in 1 year when the discount rate is 9.5% p.a.?

Which of these answers best describes an ordinary annuity?

Quiz 2: A Review of Financial Mathematics

What simple interest rate per year will give same future value at the end of 3 years as 10% p.a.compounded semi- annually?

What is the future value of a $1,000 invested for 20 years at an interest rate of 10% p.a.compounded quarterly?

What is the present value of the following set of cash flows when the discount rate is 12% p.a.compounded monthly?

What is the present value of a perpetuity consisting of payments of $500 with an interest rate of 10% p.a.?

What is the present value of an annuity consisting of 5 annual payments of $200 with an interest rate of 8% p.a.compounded annually and the first payment made immediately?

The future value in 10 years of $1,000 invested at a 10% p.a.compounded annually interest rate will be _____________ the future value in 10 years of $1,000 invested at a 10% p.a.simple interest rate.

At the end of a 5- year period,the difference between the future value of $200 invested at 8% p.a.simple interest and $200 invested at 8% p.a.compounded annually interest will be _______________

Which of the following statements is true?

What is X in the formula X = PV(1 + r) ?

What is the future value of $2,500 invested for 3 years at an interest rate of 11% p.a.compounded semi- annually?

Asset A provides a cash flow of $100 in six years' time.Asset B provides a cash flow of $100 in four years' time.Which asset would a rational investor rather own?

Which of the following will yield the highest future value at the end of 5 years?

What is the future value of $500 invested for 4 years at a simple interest rate of 5% p.a.?

What is the future value of $3,400 invested for 7 years at a simple interest rate of 7.5% p.a.?

What does the equation, (1 + r/m) m - 1,calculate?

What is the present value of an annuity due consisting of 5 annual payments of $1,000 with an interest rate of 8% p.a. ,with the first payment occurring in 5 years' time?

What is the future value of $20 invested for 80 years at an annually compounded interest rate of 7% p.a.?

What is the value of a share which is expected to pay a dividend of $0.11 every six months forever,on the basis that you intend to hold the shares forever,and the Australian ten- year bond rate today is 7.29%?

What is the present value of $1,800 to be received in 1 year when the discount rate is 9.5% p.a.?

Which of these answers best describes an ordinary annuity?

What does the equation, (1 + r/m) ^m- 1,calculate?