Chapter 5 - Time Value of Money

Question 1

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 1

c. £19,346.

FV = PV*(1+r) ^n

chapter reference 5A2

Question 2

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 2

c. 3.66%.

(1 + r/n) ^n - 1

chapter reference 5A3A

Question 3

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 3

c. 8.2%.

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

chapter reference 5A2

Question 4

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 4

d. 7.5%.

Square root to the power of (FV/PV)

chapter reference 5A2

Question 5

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 5

d. £26,058.

FV = PV*(1+r) ^n

Question 6

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 6

c. 5.09%.

(1 + r/n) ^n - 1

chapter reference 5A3A

Question 7

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 7

b. £14,201.

FV = PV*(1+r) ^n

chapter reference 5A2

Question 8

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 8

a. £3,799.59.

PV = FV / (1 + r) ^n

Question 9

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 9

c. 4.59%.

(1 + r/n) ^n - 1

chapter reference 5A3A

Question 10

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 10

d. 7.71%.

chapter reference 5A2/5A3A

Question 11

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 11

b. £2,552.56.

chapter reference 5A2

Question 12

What amount has to be invested to accumulate £1,000 at the end of 5 years at an annual interest rate of 5% compound?

Select one:

a. £746.27.
b. £942.34.
c. £783.53.
d. £801.24.

Answer 12

c. £783.53.

PV = FV / (1 + r ) ^ n

chapter reference 5A4

Question 13

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 13

b. 10.52%.

(1 + r/n) ^n - 1

(1 + 0.10 / 365) ^ 365 - 1

chapter reference 5A3

Question 14

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 14

d. 10.

chapter reference 5A1

Question 15

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 15

c. 0.055.

chapter reference 5A1

Question 16

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 16

a. 26.82%.

chapter reference 5A3A

Question 17

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 17

b. £1,448.66.

chapter reference 5A4A

Question 18

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 18

d. 3%.

chapter reference 5B

Question 19

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 19

b. 25.59%.

chapter reference 5A3A

Question 20

Simon wishes to invest a sum of money at an interest rate of 3.5% per annum to provide him with a capital lump sum of £8,000 in five years’ time. How much will he need to invest now to achieve this?

Select one:

a. £6,735.70.
b. £6,900.72.
c. £6,971.68.
d. £6,507.77.

Answer 20

a. £6,735.70.

chapter reference 5A4

Question 21

Michael’s parents plan to gift him £10,000 on his 21st birthday. Assuming they can achieve a net annual return of 5%, how much will they need to invest on his 15th birthday?

Select one:

a. £7,692.
b. £7,462.
c. £7,835.
d. £7,000.

Answer 21

b. £7,462.

chapter reference 5A4

Question 22

The nominal interest rate on a loan is 10% per annum. Interest charged at which frequency will lead to the highest annual percentage rate?

Select one:

a. Half-yearly.
b. Monthly.
c. Quarterly.
d. Daily.

Answer 22

d. Daily.

chapter reference 5A3

Question 23

On 1 October 2015 Sarah invested £25,000 in a fixed rate investment paying 4% for three years; on 1 October 2018 she reinvested the resultant sum for a further six years at a fixed rate of 5%. How much will she receive on 1 October 2024, to the nearest pound?

Select one:

a. £36,623.
b. £35,500.
c. £37,686.
d. £36,619.

Answer 23

c. £37,686.

chapter reference 5A2

Question 24

What is the annual percentage rate on a loan, where interest is charged at the rate of 18% a year on a monthly basis?

Select one:

a. 25.44%.
b. 18%.
c. 19.56%.
d. 22.5%.

Answer 24

c. 19.56%.

chapter reference 5A3A

Question 25

A deposit account pays an interest rate of 6% per annum, compounded on a monthly basis. What will the annual equivalent rate be?

Select one:

a. 6.7%.
b. 6.13%.
c. 6.17%.
d. 6.96%.

Answer 25

c. 6.17%.

chapter reference 5A3A

Question 26

A lump sum of £15,000 is invested for three years at 4% and then for a further three years at 3.5%. To the nearest pound, what will the investment be worth at the end of the term?

Select one:

a. £18,075.
b. £18,707.
c. £17,988.
d. £18,978.

Answer 26

b. £18,707.

chapter reference 5A2

Question 27

Brian’s grandparents plan to gift him £5,000 on his 18th birthday. Assuming they can achieve a net annual return of 4%, how much will they need to invest on his 13th birthday, to the nearest pound?

Select one:

a. £4,110.
b. £4,000.
c. £4,167.
d. £3,951.

Answer 27

a. £4,110.

chapter reference 5A4

Question 28

Stella invests £20,000 into a unit trust and after five years it is worth £26,263.32. What average annual rate of return has she received on this investment?

Select one:

a. 4.64%.
b. 6.26%.
c. 5.6%.
d. 15.2%.

Answer 28

c. 5.6%.

chapter reference 5A2