4 - The principles of the time value of money Flashcards
what are the four basic definitions of time value of money?
PV - present value
n - time period
r - interest rate
FV - future value
A sum of £5,000 invested over five years at a rate of 4% would give what return after 5 years?
£6083.26
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?
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%
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?
annual rate 1,000 x (1+r) = 1.10
half yearly 1,000 x 1.05 (2)
quarterly 1,000 x 1.025 (4)
When are APR and AER usually used?
APR for loans
AER for savings
Can the same fomula be used to calculate APR and EAR/AER?
Yes - = (1+r/n)n -1 (times 100 for rate)
If a loan has an interest rate of 24%, what would be the APR if interest is applied monthly?
26.82%
What amount has to be invested to accumulate £1,000 at the end of five years at a annual rate of 5%?
FV / (1 + 0.05)power of 5
1+0.05 to the power of 5 = 1.28
1000/1.28 = £783.53
If £100 was invested at a rate of 8% for 10 years what would the final value be?
Brackets first - (1+.08)10
1- = 1.58/0.08= 14.4866
x 100 = £1,448.66
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?
FV (100 + annual coupon of 6.5) 106.50
1.05 to the power of 2 = 1.1025
106/1.1025 = 96.60
- 50 at the end of year one (1+0.05)power 1 = 6.19
- 19+ 96.60 = £102.79
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?
A = P (1-(1+r)n)/r
1-(1-1.08) -10 = 0.46
- 46 - 1 = 0.54
- 54/0.08=6.7101 x 100 = £671.01
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?
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
How do you calcuate the real return after inflation is considered?
Real
Rnom
Rinf
Real = Rnom- Rinf