f = p × ((r/100)+1) ^ n

f = Future Amount (£)
p = Principal Amount (£)
r = Interest Rate (%)
n = Number of Periods
s = Type of Period (days-weeks-months-years)

If the £1000 loan was for a period of 6 months at 10% interest rate, what is the future amount?:

1771.56 = 1000 × (0.1+1) ^ 6 months

£1,000 × (1.10 × 1.10 × 1.10 × 1.10 × 1.10 × 1.10) = £1771.56

f = £1771.56
p = £1000
r = 10% (10/100 for decimal)
n = 6
s = months

p = f / ((r/100)+1) ^ n

f = Future Amount (£)
p = Principal Amount (£)
r = Interest Rate (%)
n = Number of Periods
s = Type of Period (days-weeks-months-years)

What principal amount do you need to invest, to get £2000 in 5 years at 10% interest rate?:

1241.84 = 2000 / (0.1+1) ^ 5 years

£2,000 / (1.10 × 1.10 × 1.10 × 1.10 × 1.10) = £1241.84

f = £2000
p = £1241.84
r = 10% (10/100 for decimal)
n = 5
s = years

r = (f/p) ^ 1/n - 1

f = Future Amount (£)
p = Principal Amount (£)
r = Interest Rate (%)(x100 for percentage)
n = Number of Periods
s = Type of Period (days-weeks-months-years)

You have £1,000, and want it to grow to £2,000 in 5 Years, what interest rate do you need?:

0.1487 = (2000/1000) ^ 1/5 years - 1

(£2000/£1000) ^ 1/5 - 1 = 0.1487 x 100 = 14.87%

f = £2000
p = £1000
r = 14.87% 
n = 5
s = years

(note: it uses the natural logarithm function ln)

n = ln(f/p) / ln(1+r)

f = Future Amount (£)
p = Principal Amount (£)
r = Interest Rate (%)
n = Number of Periods
s = Type of Period (days-weeks-months-years)

How many years will it take to turn £1,000 into £2,000 at 10% interest rate?:

7.27 = ln(2000/1000) / ln(1+(r/100))

ln(£2000/£1000) / ln(1+(10/100)) = 7.27 years

f = £2000
p = £1000
r = 10% (10/100 for decimal)
n = 7.27
s = years

f = p × (((r/100)/n)+1) ^ n

f = Future Amount (£)
p = Principal Amount (£)
r = Interest Rate (%)
n = Number of Periods within the year (Semiannually=2,Quarterly=4,Monthly=12,Daily=365,Continuously=2.71828182845904523536028747135266249775724709369995957
49669676277240766303535475945713821785251664274)

If £1000 was invested at 10% interest rate, "Compounded Semiannually"; what is the future amount?:

1102.5 = 1000 × (((10/100)/2)+1) ^ 2

£1000 × (((10/100)/2)+1) ^ 2 = £1102.50

f = £1102.50
p = £1000
r = 10% (10/100 for decimal)
n = 2 

e = (1+((r/100)/n)) ^ n − 1

e = Effective Annual Interest Rate (%)(x100 for percentage)
r = Nominal Interest Rate (%)
n = Number of Periods within the year (Semiannually=2,Quarterly=4,Monthly=12,Daily=365,Continuously=2.71828182845904523536028747135266249775724709369995957
49669676277240766303535475945713821785251664274)

What effective annual interest rate do you get when the ad says "6% compounded monthly"?:

0.06168 = (1+((6/100)/12)) ^ 12 − 1

0.06168 x 100 = 6.168%

e = 6.168%
r = 6% (6/100 for decimal)
n = 12 

v = p × (1 − (1+r) ^ −n) / r

v = Present Value of Annuity (£)
p = Value of Each Payment for Annuity (£)
n = Number of Periods
r = Interest Rate per Period (%)

What is the present value for annuity of £400 a month for 5 years?, use a monthly interest rate of 1%:

17982.02 = 400 x (1 - (1+(1/100)) ^ -60) / (1/100)

£400 x (1 - (1+(1/100)) ^ -60) / (1/100) = £17982.02

v = £17982.02 
p = £400
n = 60 (12 months x 5 years)
r = 1% (1/100 for decimal)

p = v × r / (1 − (1+r) ^ −n)

p = Value of Each Payment for Annuity (£)
v = Present Value of Annuity (£)
n = Number of Periods
r = Interest Rate per Period (%)

Say you have £10,000 and want to get a monthly income for 6 years out of it, 
how much could you get each month?, assume a monthly interest rate of 0.5%:

165.73 = 10000 × (0.5/100) / (1 − (1+(0.5/100)) ^ −72)

£10000 × (0.5/100) / (1 − (1+(0.5/100)) ^ −72) = £165.73

p = £165.73
v = £10000
n = 72 (12 months x 6 years)
r = 0.5% (0.5/100 for decimal)

Ganesh Niruban