Investment Formulas

Question 1

Future Value of money (simple interest)

Answer 1

FV = Principal amount x [ 1+ (r x n) ]

r = rate. Eg 5% = 0.05
N = years

Eg £2,000. Over 3 years at 5%

FV 2,000 x [ 1+ (0,05 x 3) ]. = £2,300

Question 2

Future value of money (compound interest)

Answer 2

FV = PV ( 1 + r ) n
Example:
£2,000 principal over 3 years at 5%

FV = 2,000 (1 + 0.05) 3 = £ 2315.25

Question 3

Compounding periods other than yearly

Eg Monthly or quarterly

Answer 3

If monthly, divide interest rate by 12
Eg 5% = 0.05 divided by 12 = 0.4167
3 year for monthly = 36 months compounding periods
Example £2,000 over 3 years at 0.5%

FV = 2,000 ( 1+ 0.004167) 36 = £2322.94
Better way:
2000(1+0.05/12)v36 = 2322.94

Question 4

Discounting

• What is it
• Formula

Answer 4

• Determine how much would be invested now ,given a rate and frequency of payments to meet a future required sum
• PV =FV/(1+r)n

FV - Future value ; PV - Present value ; n - number of periods ; r - rate of interest
Example
FV - £1,000
R - 0.05
N - 3

1,000/(1+0.05)v3 = £863.84

Question 5

Finding r (calculating the rate of return)

Answer 5

Example: Calculate discount rate if future projected value is £2,000 in 3 years time and present value is £1,000
FV - £2,000
PV - £1,000
,n   - 3
Basic formula FV= PV(1+r)n
2,000 = 1,000(1+r)3
2,000/1,000 = (1+r)3
3 to root of (2,000 /1,000) = 1 +r 
3 to root of(2,000 /1,000) - 1 = r

n-/ (FV /PV) - 1 = r

Nth route

Question 6

Regular premium calculation

Answer 6

PV x { ( 1+ r ) n - 1 } = FV
___________
r

Example £1,000 over 18 @ 5%

1,000 x. (1 + 0.05)^18 - 1
________________.

                         0.05

= £ 23,132.38

Question 7

Annuities

Answer 7

P x { 1 - ( 1 + r ) ^ -n } =A
______________
r

A = Present value of annuity
P = Regular annuity payment
r = interest payment
n = no.of periods

Example: P= £4K pa , r = 6% (0.06) n = 5 (years)

1. 1 - (1+ 0.06)^-5 = 0.252741827
2. Ans / 0.06 = 4.212363786
3. Ans x 4000 = 16849.46 or £16,849.46

Question 8

APR or AER

Answer 8

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

Example:
Int on monthly loan @ 21%. What is APR

APR = ( 1 + 0.21/12) ^ 12 - 1 = 23.14%

AER
Account pays 2.5% pa paid half yearly
( 1+ 0.25/2) ^2 - 1 = 2.52%

Question 9

Real rate of return
Simple version
Accurate version

Answer 9

Real return = Rnominal - Rinflation

1 + nominal. - 1
—————
1+ inflation

Question 10

Real v Nominal returns

simple
Detailed

Answer 10

Real = R nominal - R inflation

Or

1 + nominal
____________. - 1. = real rate of return
1+ inflation

Question 11

Compounded annual return (CAR)

Establish total return over number of periods. Calculate each annualised return and multiply

Answer 11

(Year 1 x Year 2 x Year 3 - 1) = Total return over 3 year period (CAR)

EXAMPLE
Year 1 : 1% , Year2 5% , Year 3 3%

CAR = (1.01) x (1.05) x (1.03) = 1.0923 = 9.23%

Question 12

HOLDING PERIOD RETURN

WHAT IS IT

Answer 12

R = D + V1 - V0
___________
V0

D = Additional returns (income/divs) V0 = Starting price V1 = end price

HPR - Measure how much investment has increased in value over period of time. Basically growth/loss of investment as percentage of start value

Question 13

What is Money Weighted Return (MWR)

Answer 13

Used to measure performance that takes into account cash deposited or withdrawn during whole period. More sophisticated that HPR.
HOWEVER, INFLUENCED BY CASH FLOWS IN AND OUT.Doesnt show whether overall return is is due to ability of manager or result of when additional funds were invested. Doesnt take into account timing
MWR:
D + V1-V0 - C
__________________________________
V0 +(C x n/12) in. + (-C x n/12) out

Question 14

Formula for working out a monthly rate if annual APR is known

Answer 14

Monthly rate = 12-/1+APR -1