# Compound Interest Calculation

The compound interest formula is an equation that Savings account. The compound interest equal to future value of the investment, in our calculation its the final balance . The initial balance multiple to 1 numbers of value added to annual interest rate divided is interest compound year multiple the numbers of year.

The annual compound interest is  formula,

Fv=p(1+r/m)^mt

let us consider,

1) FV – the future value of the investment, in our calculator it is the final balance

2.)P – the initial balance(the value of the investment)

3.)r – the annual interest rate(in decimal)m – the number of times the interest is compounded per year (compounding frequency)

4.)t – the numbers of years the money is invested for

2.)complex calculation of the value of an investment

Complex Calculation ofthe future value of an initial investment in which interest is compounded month

For Example

The initial balance p is \$10000 the number of years you are going to invest money is 10, the interest rate r is equal to 5%

FV = 10,000 * (1 + 0.05/12) ^ (10*12) = 10,000 * 1.004167 ^ 120 = 10,000 * 1.647009

The answer is FV = 16,470.09

The value of your investment after 10 years will be \$16,470.09.

FV = 10,000 * (1 + 0.05/12) ^ (10*12) = 10,000 * 1.004167 ^ 120 = 10,000 * 1.647009 = 16,470.09

FV = 10,000 * (1 + 0.05/12) ^ (10*12) = 10,000 * 1.004167 ^ 120 = 10,000 * 1.647009 = 16,470.09

## 3.) Calculating the interest rate of an investment

Eample

The initial balance p is \$ 2000 and final balance FV is \$ 3000 The time horizon of the investment 6  years and the frequency of the computing is 1.

3,000 = 2,000 * (1 + r/1) ^ (6*1)

Raise both sides to the 1/6th power

3,000 = 2,000 * (1 + r/1) ^ (6*1)

r=1.5^0.166667- 1 = 1.069913 – 1 = 0. 069913 = 6. 9913

The answer is interest rate   6.9913%.

Calculate the compound interest

FV = P (1 + r/m)^mt

m = 1, r = 4%, and ‘FV = 2 * P we can write

2P = P (1.04) ^ t

P (P mustn’t be 0!)

2 = 1.04 ^ t

t = ln(2) / ln(1.04) = 0.693147 / 0.039221 = 17.67