Compound interest is one of the most powerful forces in investing. Simple interest simply means a set percentage of the principal for the period, and is rarely used in practice. On the other hand, compound interest is applied to both loans, investments and deposit accounts.
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Calculate future amount for loan or investment
f = p × ((r/100)+1) ^ n -
Calculate principal amount for loan or investment
p = f / ((r/100)+1) ^ n -
Calculate interest rate for loan or investment
r = (f/p) ^ 1/n - 1 -
Calculate number of periods for loan or investment
n = ln(f/p) / ln(1+r) -
Calculate periodic compounding future amount for loan or investment
f = p × (((r/100)/n)+1) ^ n -
Calculate effective annual interest rate for loan or investment
e = (1+((r/100)/n)) ^ n − 1 -
Calculate present value of annuity
v = p × (1 − (1+r) ^ −n) / r -
Calculate value of each payment for annuity
p = v × r / (1 − (1+r) ^ −n)
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)
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