Some Important Formula's in Personal Finance 1. Compound Interest : 2. Annuity 3. CAGR Manish Chauhan http://www.jagoinvestor.com

1. Compound Interest :

2. Annuity

3. CAGR

Manish Chauhan

http://www.jagoinvestor.com

Compound Interest This formula is used to calculate future value of One time payment today after some years . Future Value = Present Value * (1 + rate)^Tenure Rate = Expected rate of Return Tenure = Number of years

This formula is used to calculate future value of One time payment today after some years .

Future Value = Present Value * (1 + rate)^Tenure

Rate = Expected rate of Return

Tenure = Number of years

Example 1 (Compound Interest)‏ I want to invest Rs 50,000 in a Fixed Deposit for 5 yrs at 8% rate of return . How much will be the maturity value Future Value = 50,000 * (1 + .08) ^ 5 = 73466

I want to invest Rs 50,000 in a Fixed Deposit for 5 yrs at 8% rate of return . How much will be the maturity value

Future Value = 50,000 * (1 + .08) ^ 5

= 73466

Example 2 (Compound Interest)‏ I want to invest Rs 10,000 in a mutual fund today , How much will it become after 10 yrs , considering the rate of return of 15% . Future Value = 10,000 * (1 + .15) ^ 10 = 40455

I want to invest Rs 10,000 in a mutual fund today , How much will it become after 10 yrs , considering the rate of return of 15% .

Future Value = 10,000 * (1 + .15) ^ 10

= 40455

Annuity This formula is used to calculate the future value when we do investment on a regular basis after a fixed interval . Example - when we invest in a mutual fund per month through SIP . - When we put money in our PPF account each year . Formula Future value = Amount per installment * (1+r) * [(1+r) ^n - 1]/ r

This formula is used to calculate the future value when we do investment on a regular basis after a fixed interval .

Example

- when we invest in a mutual fund per month through SIP .

- When we put money in our PPF account each year .

Formula

Future value = Amount per installment * (1+r) * [(1+r) ^n - 1]/ r

Example 1 (Annuity)‏ I want to invest Rs 50,000 in a my PPF account per year for next 15 yrs , How much will it become after 15 yrs , at 8% . Future Value = 50,000 * (1.08) * (1.08 ^ 15 - 1)/.08 = 14,66,214

I want to invest Rs 50,000 in a my PPF account per year for next 15 yrs , How much will it become after 15 yrs , at 8% .

Future Value = 50,000 * (1.08) * (1.08 ^ 15 - 1)/.08

= 14,66,214

Example 2 (Annuity)‏ I want to invest Rs 1,000 in a mutual fund per month for next 10 yrs , How much will it become after 10 yrs , considering the rate of return of 12% . r = rate of return = 12/12 = 1% (per month) n = number of payments = 12 * 10 = 120 Future Value = 1,000 * (1.01) * (1.01 ^ 120 - 1)/.01 = 232339

I want to invest Rs 1,000 in a mutual fund per month for next 10 yrs , How much will it become after 10 yrs , considering the rate of return of 12% .

r = rate of return = 12/12 = 1% (per month)

n = number of payments = 12 * 10 = 120

Future Value = 1,000 * (1.01) * (1.01 ^ 120 - 1)/.01

= 232339

CAGR : Compounded annual Growth Rate - Used to calculate the annual Return provided by an Investment . - Tool to compare investments - Opposite of Compound Interest Formula CAGR = nth root of [(Current Value / Original Investment) -1 n = tenure nth root = to the power 1/n

- Used to calculate the annual Return provided by an Investment .

- Tool to compare investments

- Opposite of Compound Interest

Formula

CAGR = nth root of [(Current Value / Original Investment) -1

n = tenure

nth root = to the power 1/n

Example 1 (CAGR)‏ I Invested Rs 50,000 in a mutual fund on June 2005 , Its value after 4 yrs is Rs 1,00,000 . What is the annual returns it has provided to me ? CAGR = [(100000 /50000)^ (1/4) - 1 ] = 2 ^ .25 - 1 = .1892 = 18.92% Annual return

I Invested Rs 50,000 in a mutual fund on June 2005 , Its value after 4 yrs is Rs 1,00,000 . What is the annual returns it has provided to me ?

CAGR = [(100000 /50000)^ (1/4) - 1 ]

= 2 ^ .25 - 1

= .1892

= 18.92% Annual return

Example 2 (CAGR)‏ Which investment is Better ? Investment 1 : 50,000 invested in 2000 became 2,00,000 in 2009 Investment 2 : 10,000 invested in 2004 became 25,000 in 2008 CAGR for Investment 1 = [200000/50000]^(1/9) - 1 = 16.65 % CAGR for Investment 2 = [25000/10000] ^ (1/4) - 1 = 25.74% Hence , Investment 2 is better than Investment 1 .

Which investment is Better ?

Investment 1 : 50,000 invested in 2000 became 2,00,000 in 2009

Investment 2 : 10,000 invested in 2004 became 25,000 in 2008

CAGR for Investment 1 = [200000/50000]^(1/9) - 1

= 16.65 %

CAGR for Investment 2 = [25000/10000] ^ (1/4) - 1

= 25.74%

Hence , Investment 2 is better than Investment 1 .

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