l3&4 : time value of money Flashcards
what is future value?
the amount a sum of money grows to be, as it earns interest over a period
if i invest £1000 at 12% per year, what is the FV at the end of 1 year?
FV = 1000 x (1 + 0.12)
FV = £1120
if i invest £1000 at 12% per year, what is the FV at the end of 2 years?
FV = 1000 x 1.12 x 1.12
FV = £1254.40
what is the PV to give £2000 in 5 years time at a rate of 11%?
PV x (1.11)^5 = 2000
PV = 2000 / (1.11)^5
PV = £1186.90
give the formula for future value (FV) in terms present value (PV), interest rate (r) and time period (t).
FV = PV (1+r)^t
give the formula for time period (t) in terms of future value (FV), present value (PV) and interest rate (r).
t = ln (FV/PV) / ln (1+r)
give the formula for interest rate (r) in terms of future value (FV), present value (PV) and time period (t).
r = [FV/PV]^(1/t) -1
calculate r if your investment doubles in 5 years.
r = [2/1]^(1/5) -1
r = 14.87%
given that r = 30%, calculate how long it will take to double your money.
t = ln (2/1) / ln (1+0.3)
t = 2.64 years
what is an annuity?
a series of regular and constant cash flows for a period
calculate the PV of a 6year annuity of £4000 at r = 8%.
PV = C x 1 - [1/(1+r)^t]
——————
r
PV = 4000 x 1 -[1/(1.08)^6]
——————-
0.08
PV = £18491.50
you borrow £30,000 at an interest rate of 12% and plan to repay the loan using a 10 year annuity. calculate the annual repayment.
PV = C x 1 - [1/(1+r)^t]
——————
r
30000 = C x 1 - [1/(1.12)^10]
———————-
0.12
C = 30000 / 5.65
C = £5309.50
what is a perpetuity?
an annuity where the cash flows continue forever. essentially there is no t value.
give the equation to calculate annuity.
PV = C x 1 - [1/(1+r)^t]
——————
r
give the equation to calculate perpetuity.
PV = C / r
