Please help Can you please explain in detail Explain the con

Please help. Can you please explain in detail.

Explain the concept of compound interest and its relation to exponential functions.

One very important exponential equation is the compound-interest formula:

A = P (1 + r/n) ^ (nt)

Solution

Exponential functions are used in variety of formulas.One such case is compound interest

Compund interest is calculated by A(t) = P( 1+r/n)^nt

where P ---principal amount invested

r ----rate of ineterst

n --- compounding number of times the interest is compounded per year ,whether yearly n=1, half yearly n= 2 , monthly n=12

t --- no. of years

If Compounded Continuously Interest: is calculated by the formula then we use another formula:

A(t) = P e^rt

Example : let the interest rate r be 4%, compounded monthly, and let the initial investment amount be $1200. Then the compound-interest equation, for an investment period oft years, becomes:

A(t) = 1200( 1+ 4/12)^12t

= 1200(1.33)^(12t)