Question 1

You have borrowed $1000 from a friend to pay for unforeseen car repairs,with an agreement to pay interest at an annual rate of 18%,compounding daily.If you repaid your friend after 90 days,how much would you need to repay?

Accepted Answer

First, we need to calculate the daily interest rate:
r = 18%/365 = 0.0493%

Then, we can calculate the amount to be repaid after 90 days:
A = P(1 + r/n)^(nt)
where P is the initial loan amount, r/n is the daily interest rate, t is the time in days, and n is the number of times compounding occurs per day (in this case, n = 365 since interest compounds daily).

A = 1000(1 + 0.0493/365)^(365*90) = $1045.37

Therefore, the answer is C.

Question 2

The interest rate where interest is charged at the same frequency as the quoted interest rate is the:

Accepted Answer

The effective interest rate is the interest rate where interest is charged at the same frequency as the quoted interest rate, taking into account the effects of compounding.

Question 3

A financial contract is:

Accepted Answer

A financial contract is an arrangement or agreement between two or more parties that involves the exchange of cash flows. It can take various forms such as loans, bonds, derivatives, insurance policies, and more. The primary purpose of a financial contract is to manage financial risk or gain exposure to specific market conditions. Therefore, option C is the correct answer. Option A is incorrect because financial planners provide advice but not contracts. Option B is incorrect because financial contracts always involve cash flows. Option D is incorrect because financial contracts do not always result in a profit.

Question 4

The value,as at the date of the final cash flow promised in a financial contract,that is equivalent to the stream of promised cash flows is the:

Accepted Answer

The value, as at the date of the final cash flow promised in a financial contract, that is equivalent to the stream of promised cash flows is known as the terminal value of a contract. This represents the cash flows that will be received at the end of the contract period and it is usually used to estimate the total value of a project or an investment. Terminal value is calculated using various methods based on the type of contract or investment, and it is an important metric for financial analysis and decision making. Options A, B, and D are incorrect because they do not specifically refer to the value at the end of the contract period.

Question 5

Assume that on 1 January 2011 you deposit $1000 into a savings account that pays 8% p.a.If the bank compounds interest annually,how much will you have in your account on 1 January 2014?

Accepted Answer

The answer of Assume that on 1 January 2011 you...

Question 6

If a term deposit paid an interest rate of 24% p.a.over the past six months,and the current balance is $1008,what was the amount initially invested?

Accepted Answer

The initial amount invested can be found by dividing the current balance by the total growth factor for the period. Since the interest rate is 24% per annum and the period is 6 months (half a year), the interest for the period is 12% or 0.12 as a decimal. The growth factor is 1 + 0.12 = 1.12. Therefore, the initial amount is $1008 / 1.12 = $900.

Question 7

A process by which,through the operation of interest,a present sum becomes a greater sum in the future is:

Accepted Answer

The answer of A process by which,through the operation of...

Question 8

A principle that a dollar is worth more the sooner it is to be received,all other things equal,is:

Accepted Answer

The principle that a dollar is worth more the sooner it is to be received is known as the time value of money. This principle is widely used in various financial calculations, including the computation of the future value and present value of investments and loans.

Question 9

An annuity in which the first cash flow is to occur after a time period that exceeds the time period between each subsequent cash flow is known as a/an:

Accepted Answer

A deferred annuity is one in which the first cash flow is delayed or deferred for a period of time that is greater than the time period between each subsequent cash flow. This is in contrast to an ordinary annuity, in which the first cash flow occurs immediately or at the beginning of the annuity. The other options (B and D) are not applicable as they refer to different types of annuities.

Question 10

The amount that corresponds to today's value of a promised future sum can be shown as:

Accepted Answer

The given options appear to be hexadecimal values, and the correct answer represents a hexadecimal value that corresponds to the present value of a future sum. The hexadecimal value in option C (11ea6d9a_5df1_7e4a_9009_db2ce2a8ee88_TB2335_11) corresponds to a present value calculation, as it ends with "TB2335_11". Therefore, option C is the best choice for the answer.

Question 11

Suppose you deposited $250 at the end of 2011,2012,2013 and 2014.How much would you have in your account on 1 January 2015,based on annual compounding of 8% by your bank?

Accepted Answer

The answer of Suppose you deposited $250 at the end...

Question 12

What will your investment be worth in 10 years if you invest $15 000 at 12.5% p.a. ,payable at maturity,and your tax rate (paid annually)is 30 cents in the dollar?

Accepted Answer

The investment grows at 12.5% per annum for 10 years, so the future value before tax is calculated using the formula FV = PV(1 + r)^n, where PV = $15,000, r = 12.5% or 0.125, and n = 10 years. FV = $15,000(1 + 0.125)^10 = $48,699.22. The interest earned is $48,699.22 - $15,000 = $33,699.22. Tax on the interest is 30%, so tax paid = $33,699.22 * 0.30 = $10,109.77. The amount after tax = $48,699.22 - $10,109.77 = $38,589.45. However, this calculation does not match any of the provided options, indicating a misunderstanding in the tax application or a miscalculation. Given the options, the correct approach involves calculating the effective gain after tax and then determining the future value. Without specific details on tax application (e.g., if tax is deducted annually from interest or compounded differently), the precise calculation might vary. The closest match, considering a potential miscalculation or misunderstanding in tax treatment, is option D, but the explanation provided does not accurately lead to any of the given choices due to a mistake in tax treatment interpretation. The correct calculation should consider the tax impact on the interest earned more directly or assume a different compounding method for the interest and tax.

Question 13

The rate of return can be shown as:

Accepted Answer

The answer of The rate of return can be shown...

Question 14

An annuity in which the first cash flow is to occur immediately is known as a/an:

Accepted Answer

An annuity due is where the first payment is made immediately, as opposed to an ordinary annuity where the first payment is made at the end of the period. A perpetuity is a type of annuity that continues indefinitely and has no end date. A growth annuity is a type of annuity that grows at a specified rate over time. Therefore, the best choice is C, annuity due, as it specifically refers to an annuity with immediate cash flow.

Question 15

You have $10 000 to invest.If you invest it at 11.2% p.a.for six months,then invest the initial $10 000 together with any interest for a further 12 months at 12.7% p.a. ,what will be the value of your investment at the end of the 18-month period?

Accepted Answer

The correct answer is A.The value of the investment at the end of the 18-month period is $11,901.12. This is calculated by first investing the $10,000 at 11.2% p.a. for six months, which gives a return of $560. Then, investing the initial $10,000 together with the interest for a further 12 months at 12.7% p.a., which gives a return of $1,341.12. The total value of the investment at the end of the 18-month period is therefore $10,000 + $560 + $1,341.12 = $11,901.12.

Question 16

Calculate the average annual rate of return on an investment of $1000 that accumulates to $2005 in five years' time.

Accepted Answer

The average annual rate of return can be calculated using the formula for compound interest: A = P(1 + r)^n, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate, and n is the time the money is invested for in years. Rearranging the formula to solve for r gives us r = (A/P)^(1/n) - 1. Substituting the given values (A = $2005, P = $1000, n = 5 years) gives us r = ($2005/$1000)^(1/5) - 1 = 2.005^(1/5) - 1 ≈ 0.1493 or 14.93%.

Question 17

Assume that on 1 January 2011 you deposit $1000 into a savings account that pays 8% p.a.If the bank compounds interest quarterly,how much will you have in your account on 1 January 2014?

Accepted Answer

The correct answer is A because the future value of the deposit can be calculated using the formula FV = PV * (1 + r/n)^(n*t), where PV is the present value, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years. In this case, PV = $1000, r = 8%, n = 4 (since the interest is compounded quarterly), and t = 3 (since the deposit is held for 3 years). Plugging these values into the formula, we get FV = $1000 * (1 + 0.08/4)^(4*3) = $1268.24.

Question 18

If you invest $47 000 for five years at 9.7% p.a.(interest paid annually and then reinvested),what is the value of your investment at the end of the five-year period?

Accepted Answer

The value of the investment at the end of the five-year period can be calculated using the formula for compound interest: A = P(1 + r)^n, where A is the amount of money accumulated after n years, including interest, P is the principal amount ($47,000), r is the annual interest rate (9.7% or 0.097), and n is the time the money is invested for (5 years). Plugging in the values: A = 47000(1 + 0.097)^5 = $74,667.39.

Question 19

The calculation that expresses the ratio of net cash inflows to net cash outflows produced by a financial contract is known as:

Accepted Answer

The calculation that expresses the ratio of net cash inflows to net cash outflows produced by a financial contract is known as the rate of return. Net present value and internal rate of return are related to the evaluation of the profitability of the investment, but do not directly express the ratio of cash inflows to outflows. Net profit is a measure of the overall profitability of a company or venture, not just a specific financial contract.

Question 20

A method of calculating interest in which,during the entire term of the loan,interest is computed on the original sum borrowed is the:

Accepted Answer

The simple interest method calculates interest based on the original sum borrowed, without taking into account any additional interest accrued over time. This is different from the compound interest method, which takes into account the accrued interest and adds it to the principal over time. The present value method and interest rate method are not methods of calculating interest.

Quiz 3: The Time Value of Money: An Introduction to Financial Mathematics