Calculation Q's

Question 1

Anil buys a corporate bond and pays a clean price of £113.60 for a £100 nominal value of stock paying 7% coupon. Assuming it has exactly four years to run to maturity and had an original term of eight years, the gross redemption yield will be:

Select one:

a. 3.17%.
b. 2.76%.
c. 2.69%.
d. 3.88%.

Answer 1

a. 3.17%.

Yield = 7/113.60 = 6.16%

GRY = 6.16 - ((13.6/4)/113.40) * 100 = 3.17%

Question 2

An investor pays a clean price of £114.60 for £100 nominal value of stock with a 5.5% coupon. Assuming the stock has exactly four years to run until maturity, what will the gross redemption yield be?

Select one:

a. 1.61%.
b. 4.8%.
c. 3.19%.
d. 3.65%.

Answer 2

Yield = 5.5/114.60 = 4.8%

GRY = 4.8 - ((14.60/4)/114.60) * 100 = 1.61%

chapter reference 1C4B

Question 3

Graham has a gilt where the clean price is £95, the coupon is 5% and the time to redemption is 10 years. This means that the:

Select one:

a. redemption yield is 5.26%.
b. running yield is 4.75%.
c. running yield is 5%.
d. redemption yield is 5.79%.

Answer 3

d. redemption yield is 5.79%

chapter reference 1C4B.

Question 4

Erica has a buy-to-let property. The purchase price was £200,000 and associated costs of purchase were £30,000. The rental income is £800 per month with a 15% management fee. The headline gross yield is:

Select one:

a. 4.17%.
b. 3.55%.
c. 4.08%.
d. 4.8%.

Answer 4

d. 4.8%.

chapter reference 2B2

Headline gross yield = Gross rent / market price

= (£800 * 12) / 200,000

If we were calculating for all expenses:

Gross rent - expenses / market price + cost of buying

= ((£800 - 120) * 12) / (£200,000 + £30,000) * 100 = 3.55%

Question 5

The following information is extracted from the balance sheet of a company: issued share capital £50m, reserves £120m, current assets £70m, fixed assets £200m, current liabilities £40m, long-term debt £60m. The nominal value of the shares is £1 each. What is the net asset value [NAV] per share?

Select one:

a. £5.80.
b. £1.
c. £4.60.
d. £3.40.

Answer 5

d. £3.40.

chapter reference 2A5E

Net assets = Total assets - Total liabilities

£270m - £100m = £170m

NAV per share = Net assets / shares outstanding

£170m / 50 m shares = £3.40 NAV per share

Question 6

On 1 September 2015 Anna invested £15,000 in a fixed rate investment paying 4% for four years; on 1 September 2019 she reinvested the resultant sum for a further two years at a fixed rate of 5%. How much will she receive on 1 September 2021?

Select one:

a. £20,101.
b. £19,140.
c. £19,346.
d. £18,900.

Answer 6

c. £19,346.

FV = PV*(1+r) ^n

chapter reference 5A2

Question 7

A bank account pays an interest rate of 3.6% per annum, compounded on a monthly basis. What will the annual equivalent rate be?

Select one:

a. 3.96%.
b. 3.62%.
c. 3.66%.
d. 3.72%.

Answer 7

c. 3.66%.

(1 + r/n) ^n - 1

chapter reference 5A3A

Question 8

AER

Answer 8

AER = (1 + r/n) ^n - 1

Question 9

Warren invested £8,000 into his unit trust six years ago and it is now worth £12,837. What average annual compound rate of return has he received on this investment?

Select one:

a. 9.92%.
b. 5.47%.
c. 8.2%.
d. 10.08%.

Answer 9

c. 8.2%.

Square root to the power of (FV/PV) - 1

chapter reference 5A2

Question 10

Average annual compount rate

Answer 10

Square root to the power of (FV/PV) - 1

Question 11

James invested £6,000 into his unit trust seven years ago and it is now worth £9,954. What average annual compound rate of return has he received on this investment?

Select one:

a. 9.4%.
b. 13.5%.
c. 6.5%.
d. 7.5%.

Answer 11

d. 7.5%.

Square root to the power of (FV/PV) - 1

chapter reference 5A2

Question 12

On 1 July 2016 Henry invested £20,000 in a fixed rate investment paying 3% for four years. On 1 July 2020 he reinvests the resultant sum for a further three years at a fixed rate of 5%. How much will he receive on 1 July 2023?

Select one:

a. £24,597.
b. £25,760.
c. £28,142.
d. £26,058.

Answer 12

d. £26,058.

FV = PV*(1+r) ^n

Question 13

A bank account pays an interest rate of 5% per annum, compounded on a quarterly basis. What will the annual equivalent rate be?

Select one:

a. 5.12%.
b. 5.25%.
c. 5.09%.
d. 4.91%.

Answer 13

c. 5.09%.

(1 + r/n) ^n - 1

chapter reference 5A3A

Question 14

On 1 November 2016 Sally invested £10,000 in a fixed rate investment paying 4% for three years; on 1 November 2019 she reinvested the resultant sum for a further four years at a fixed rate of 6%. How much will she receive on 1 November 2023?

Select one:

a. £15,306.
b. £14,201.
c. £13,933.
d. £23,874.

Answer 14

b. £14,201.

FV = PV*(1+r) ^n

chapter reference 5A2

Question 15

Henry’s bank is offering a fixed rate deposit of 4% over seven years. How much will he need to invest on day one to accumulate exactly £5,000 at the end of the fixed term?

Select one:

a. £3,799.59.
b. £3,906.25.
c. £3,600.
d. £3,951.57.

Answer 15

a. £3,799.59.

PV = FV / (1 + r) ^n

Question 16

PV

Answer 16

PV = FV / (1 + r) ^n

Question 17

A building society account pays an interest rate of 4.5% per annum, compounded on a monthly basis. What will the annual equivalent rate be?

Select one:

a. 4.61%.
b. 4.55%.
c. 4.59%.
d. 4.57%.

Answer 17

c. 4.59%.

(1 + r/n) ^n - 1

chapter reference 5A3A

Question 18

Jim has a structured product that pays 145% of the amount invested at the end of 5 years. What is the AER?

Select one:

a. 9.54%.
b. 7%.
c. 8.83%.
d. 7.71%.

Answer 18

d. 7.71%.

Square root of the FV/PV - 1

chapter reference 5A2/5A3A

Question 19

A sum of £2,000 invested over 5 years with an interest rate of 5% compound would be worth how much at the end of the term?

Select one:

a. £2,680.19.
b. £2,552.56.
c. £2,500.
d. £3,000.

Answer 19

b. £2,552.56.

chapter reference 5A2

Question 20

What is the effective annual rate of interest, where the nominal rate is 10% and interest is calculated daily?

Select one:

a. 10.47%.
b. 10.52%.
c. 10%.
d. 10.25%.

Answer 20

b. 10.52%.

(1 + r/n) ^n - 1

(1 + 0.10 / 365) ^ 365 - 1

chapter reference 5A3

Question 21

In time value of money calculations, where the present value is £20,000, the interest rate is 8.2% and the time frame for investment is 10 years, ‘n’ is:

Select one:

a. £20,000.
b. 8.2%.
c. 0.082.
d. 10.

Answer 21

d. 10.

chapter reference 5A1

Question 22

In time value of money calculations, where the present value is £10,000, the interest rate is 5.5% and the time frame for investment is 8 years, ‘r’ is:

Select one:

a. 5.5%.
b. 8.
c. 0.055.
d. £10,000.

Answer 22

c. 0.055.

chapter reference 5A1

Question 23

What is the APR on a loan where interest is charged at the rate of 24% a year on a monthly basis?

Select one:

a. 26.82%.
b. 48.02%.
c. 24.94%.
d. 12.47%.

Answer 23

AER = (1 + r/n) ^n - 1

Question 24

If £100 is invested at the end of each year at an interest rate of 8% a year for 10 years, what will be the accumulated or future value at the end of 10 years?

Select one:

a. £1,627.39.
b. £1,448.66.
c. £1,564.55.
d. £1,600.

Answer 24

b. £1,448.66.

FV = P ( ( 1 + r ) ^n - 1) / r ))

chapter reference 5A4A

Question 25

FV with regular payment

Answer 25

FV = P ( ( 1 + r ) ^n - 1) / r ))

Question 26

If the nominal rate of return on an investment is 6% and inflation is 3%, what is the approximate real rate of return?

Select one:

a. 4.5%.
b. 4%.
c. 3.5%.
d. 3%.

Answer 26

d. 3%.

chapter reference 5B

Question 27

Madge has a 3 year loan with an annual interest rate of 23% payable on a monthly basis. What is the APR?

Select one:

a. 25.85%.
b. 25.59%.
c. 24.81%.
d. 30.75%.

Answer 27

b. 25.59%.

chapter reference 5A3A

Question 28

GRY

Answer 28

Interest yield + - * (gain (or loss) / number of years to maturity) / (clean price) * 100