Question 1

In an interest-only loan,the principle reduces by a small amount at first,and more rapidly towards the end of the loan.

Accepted Answer

In an interest-only loan, the principle does not reduce at all during the loan term. Only the interest is paid, and the borrower is responsible for repaying the entire principal at the end of the loan term.

Question 2

An individual borrowed $100 000 at a fixed interest rate of 12% p.a.for the entire loan term of 20 years.If the loan is to be repaid through equal monthly instalments,then the regular repayment to the nearest dollar is $1101.

Accepted Answer

We can use the formula for calculating the monthly payment on a loan based on its principal, interest rate, and term:

PMT = P * r * (1+r)^n / [(1+r)^n - 1]

where PMT is the monthly payment, P is the principal (the amount borrowed), r is the monthly interest rate (the annual rate divided by 12), and n is the total number of payments (the term multiplied by 12).

Plugging in the given values, we get:

PMT = 100000 * 0.01 * (1+0.01)^240 / [(1+0.01)^240 - 1]
    ≈ 1100.65

Rounding to the nearest dollar, the regular repayment is $1101. Therefore, the statement is true.

Question 3

If you have a choice to earn simple interest on $20 000 for three years at 9% or annually compounding interest at 8.5% for three years which one will pay more interest and by how much?
A)Simple interest by $50.00
B)Compound interest by $122.97
C)Compound interest by $145.78
D)Simple interest by $150.00

Accepted Answer

For simple interest:
I = P*r*t = 20000*0.09*3 = $5400
For compound interest:
Amount = P*(1+r)^t = 20000*(1+0.085)^3 = $25,578.22
Interest = Amount - Principal = $25,578.22 - $20,000 = $5,578.22
Therefore, the compound interest will be more by $5,578.22 - $5400 = $1178.22, which is closest to option C ($145.78). Hence, option C is the best choice.

Question 4

The nominal interest rate is difference between the inflation rate and the real rate of interest.

Accepted Answer

The nominal interest rate is the sum of the inflation rate and the real rate of interest.

Question 5

If expected inflation over the next year is 2%,and CBank requires a real rate of return of 4% per annum on housing loans,what is the nominal rate of return that CBank will charge on home loans?

Accepted Answer

The answer of If expected inflation over the next year...

Question 6

The ______ interest rate is an interest rate calculated after taking out the effects of inflation.

Accepted Answer

The answer of The ______ interest rate is an interest...

Question 7

Continuous interest rates are an example of where the future sum grows _____________.

Accepted Answer

The answer of Continuous interest rates are an example of...

Question 8

Joe has to pay $50 000 in 1.5 years' time.If the interest rate is 15% p.a. ,compounded continuously,how much does she owe in present value terms?
A)$46 387
B)$49 077
C)$39 926
D)$37 041

Accepted Answer

We can use the continuous compounding formula to find the present value:
PV = FV/e^(rt)
Where PV is the present value, FV is the future value, r is the interest rate, and t is the time.
Plugging in the values, we get:
PV = 50000/e^(0.15*1.5)
PV = $39,925.90
Therefore, Joe owes $39,926 in present value terms. The closest option is choice C.

Question 9

You are planning a six month around-the-world trip in 2 years' time.You estimate that you will need $30 000 to pay for the trip.To accumulate this future amount you plan to deposit an equal amount in the bank each month,which will earn 9% nominal interest per annum compounded monthly.Your first payment will be made at the end of the first month.
a.How much must you deposit each month to accumulate the $30 000?
b.What is the effective annual rate of interest that corresponds to this nominal rate?
c.If you could instead make a lump sum payment today instead of monthly payments,how much would this sum have to be to reach $30 000 in two years if it earns a nominal 9% per annum compounded monthly?

Accepted Answer

The answer of You are planning a six month around-the-world...

Question 10

A principle-and-interest loan is a common example of an __________ annuity.

Accepted Answer

The answer of A principle-and-interest loan is a common example...

Question 11

The annuity where the cash flows continue forever is called a ________.

Accepted Answer

The answer of The annuity where the cash flows continue...

Question 12

Peter borrowed $5000 and 18 months later repays the loan with a single payment of $6400.
a.What is the implied annual simple interest rate?
b.What is the implied annual compound interest rate?

Accepted Answer

The answer of Peter borrowed $5000 and 18 months later...

Question 13

A lender offers a nominal interest rate on a loan of 6% p.a.compounding quarterly.This corresponds to an effective interest rate of 6.136%.

Accepted Answer

The formula for converting from nominal to effective interest rate with quarterly compounding is:

Effective interest rate = (1 + i/n)^n - 1
where i is the nominal interest rate and n is the number of compounding periods per year.

Using this formula, we have:

Effective interest rate = (1 + 0.06/4)^4 - 1 = 0.06136 or 6.136%

Therefore, the statement is true.

Question 14

The term ______________ is used to describe the 'rate of return' when the financial contract is in the form of debt.

Accepted Answer

The answer of The term ______________ is used to describe...

Question 15

An __________ interest rate is one where the frequency of payment does not match the time period specified by the interest rate.

Accepted Answer

The answer of An __________ interest rate is one where...

Question 16

An individual is offered the sum of $100 000 to be received after 5 years.If the relevant interest rate is 8% p.a. ,compounding annually,then the present value of this promised sum is $68 058.32.

Accepted Answer

The present value (PV) is calculated using the formula PV = FV / (1 + r)^n, where FV is the future value ($100,000), r is the interest rate (0.08), and n is the number of years (5). Plugging in these values gives PV = $100,000 / (1.08)^5 = $68,058.32.

Question 17

You have an outstanding car loan of $300 per month for the next 2 years.As you are finishing your studies this year,it would be better if you could pay the full sum at the end of two years.If the interest rate on the loan is 6% per annum (compounded monthly),what final sum would the bank require at the end of two years so that it is indifferent between the two methods of payment?

Accepted Answer

The answer of You have an outstanding car loan of...

Question 18

The distinguishing feature of an annuity due is that the time period between the payment of each successive cash flow differs to the frequency with which the interest compounds.

Accepted Answer

The distinguishing feature of an annuity due is that the first cash flow occurs at the beginning of the period, rather than at the end as with a regular annuity. The time period between successive cash flows is the same, regardless of how frequently the interest compounds.

Question 19

Your parents give you $120 per week for living expenses while you are doing a three-year degree in finance.If the interest rate is 6.5% per annum,what is this cash flow worth when you start your degree?
A)$15 125
B)$16 998
C)$26 026
D)$27 330

Accepted Answer

The answer of Your parents give you $120 per week...

Question 20

What is the difference between daily and monthly compounding for a nominal interest rate of 7% per annum?
A)0.06%
B)0.04%
C)0.02%
D)0.01%

Accepted Answer

Daily compounding results in slightly more interest than monthly compounding due to more frequent application of interest. The difference between daily and monthly compounding for a 7% nominal rate is approximately 0.02%.

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