Question

6. A nominal annual rate which indicates a compounding frequency:

Select one:

A. Allows us to determine the effective rate for any smaller period less than a year, by simply dividing the annual rate by the number of those smaller periods that occur in a year.

B. Allows us to determine the effective rate for the period that matches the compounding frequency, by dividing the annual rate by the number of times interest compounds in a year.

C. Makes it impossible to determine the effective rate for periods smaller than a year.

D. Only allows us to determine the effective annual rate but not effective rates for smaller periods.

7. Which of the following is CORRECT? When discounting an amount to be received in one years' time at a rate that is quoted as 12% compounding quarterly, we can:

Select one:

A. Discount the amount using an effective monthly rate of 1% where the number of periods is 12.

B. Discount the amount using an effective annual rate (EAR) of (1+0.01)^12-1 =12.6825% where number of periods is 1.

C. Discount the amount using the annual rate of 12% where number of periods is 1.

D. Discount the amount using the effective quarterly rate of 3% where the number of discount periods is 4.

8.You invest in your savings account $2365 today, $2000 at the end of year one and $3900 at the end of year three. If the interest rate is 6.1% per annum, compounded annually, then the amount you will have in exactly three years is closest to:

Select one:

a. $8976.17

b. $8754.34

c. $9214.07

d. $8846.73

9.Jack deposits the following amounts in a savings plan which pays 9.6% per annum, compounded monthly:

• $2853 today,
• $1400 at the end of year two and
• $2000 at the end of year three.

The amount he will have in exactly 3 years is closest to:

Select one:

a. $7495.90

b. $7290.47

c. $7341.33

d. $6994.73

11.Jack sells his lawn-mowing business for $50,000 but the buyer wants to pay for it in two cash payments: $25,000 in two months from today and the balance in 1 year from today. How much will Jack need to receive as the final payment (in 12 months) if the interest rate he charges is 6% per annum compounding monthly?

Select one:

A. $25,584.91

B. $25,248.14

C. $27,446.42

D. $26,805.39

13.You owe your parents $40,000 (in present day dollars) and want to repay them in equal amounts the first to occur in 4 years from today and the other in 6 years from today. If the interest rate is 4.8% per annum compounding monthly, what will be the amount of each repayment?

Select one:

A. $25,383.68

B. $21,000.00

C. $25,255.69

D. $24,956.22

15. An advertised investment product promises to pay $597 per month for 51 months commencing in 1 month from today. If the investment earns 8.0% p.a compounding monthly, how much will the investment product cost today? (round to nearest cent; don’t use $ sign or commas)

Select one:

a. $2248.42

b. $25739.01

c. $2081.87

d. $25910.60

17. A bank offers personal loans at 12.7%p.a compounding monthly. The effective annual rate of interest (EAR) is ( to the nearest two decimal places):

Select one:

a. 1.06%

b. 13.32%

c. 13.10%

d. 13.47%

Answer 1

6.

Correct Answer is Option B

An interest rate takes two forms: Nominal interest rate and Effective interest rate.

The nominal interest rate does not take into account the compounding period, whereas, the effective interest rate takes into account the compounding period.

In order to compute the effective rate for the period that matches the compounding frequency, from the nominal interest rate, we have to divide the Nominal Rate or Annual rate by the number of times interest compounds in a year.

For example, let the Nominal interest rate be 10% which is compounded 4 times in a year

Hence, effective rate for each period we have to divide 10% by 4 i.e = (10% / 4) = 2.5%

Hence, 2.5% per period is the effective rate.

Option A is incorrect, because to determine the effective rate, we have to divide the nominal Rate or Annual Rate by the number of times interest compounds in a year. We cannot merely divide the Annual Rate or Nominal rate with the number of those smaller periods, as interest may not compound in those smaller periods.

Option C is incorrect as effective rate for periods smaller than a year can be determined

Option D is also incorrect as both effective annual rate and effective rates for smaller periods can be determined