4 - The principles of the time value of money

Question 1

what are the four basic definitions of time value of money?

Answer 1

PV - present value
n - time period
r - interest rate
FV - future value

Question 2

A sum of £5,000 invested over five years at a rate of 4% would give what return after 5 years?

Answer 2

£6083.26

Question 3

A client invests £10,000 into a until trust, after 5 years it is worth £15,785. What is the compound rate of return achieved in a year?

Answer 3

FV (15,875) = £10,000 + r)5

15875/10000 = 1.5875
5th square root of 1.5875 = 1.0956
1.0956 -1 = 0.956 x 100 = 9.56%

Question 4

If £1000 is invested for 1 year and the nominal rate (annual rate) is 10%, what would the return be if interest was paid half yearly and quarterly?

Answer 4

annual rate 1,000 x (1+r) = 1.10
half yearly 1,000 x 1.05 (2)
quarterly 1,000 x 1.025 (4)

Question 5

When are APR and AER usually used?

Answer 5

APR for loans

AER for savings

Question 6

Can the same fomula be used to calculate APR and EAR/AER?

Answer 6

Yes - = (1+r/n)n -1 (times 100 for rate)

Question 7

If a loan has an interest rate of 24%, what would be the APR if interest is applied monthly?

Answer 7

26.82%

Question 8

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

Answer 8

FV / (1 + 0.05)power of 5

1+0.05 to the power of 5 = 1.28

1000/1.28 = £783.53

Question 9

If £100 was invested at a rate of 8% for 10 years what would the final value be?

Answer 9

Brackets first - (1+.08)10
1- = 1.58/0.08= 14.4866
x 100 = £1,448.66

Question 10

A bond pays 6.5% annual coupon and is redeemable at its par or nominal value of £100 in two years time. The interest is 5% per annum, what is the theoretical price of the bond?

Answer 10

FV (100 + annual coupon of 6.5) 106.50

1.05 to the power of 2 = 1.1025
106/1.1025 = 96.60

6. 50 at the end of year one (1+0.05)power 1 = 6.19
7. 19+ 96.60 = £102.79

Question 11

How much needs to be invested as a lump sum to provide an annual payment of interest and capital of £100 at the end of each year for 10 years if the interest earned is 8% per year?

Answer 11

A = P (1-(1+r)n)/r

1-(1-1.08) -10 = 0.46

0. 46 - 1 = 0.54
1. 54/0.08=6.7101 x 100 = £671.01

Question 12

Sam has £30K invested in a building society paying 3% per year. Interest is credited monthly, so that at the end of the six years the account will have a nil balance, how much can Sam withdraw at the end of each month?

Answer 12

6 years is 72 months
Monthly interest 3% /12 = 0.25%
30K = P (1-(1.0025)n -72) / 0.0025

30K = 1- 0.1645/0.0025

30K/65.819 = £455.81

Question 13

How do you calcuate the real return after inflation is considered?

Answer 13

Real
Rnom
Rinf

Real = Rnom- Rinf