**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

**Answer**

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

**Answer**

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

**Answer**

The answer is compound interest 17.67%