Mathematics: The formula a=p(1+r)t is used to show the total amount owed for a loan with a simple annual interest rate. solve for r.

The formula a=p(1+r)t is used to show the total

chrisraptorofficial

12.03.2022

$r=(\frac{A}{P})^{\frac{1}{t}}-1$

Step-by-step explanation

Compound interest is the addition of interest to the principal sum of a deposit or a loan.

Let P = principal amount which was taken as a loan then the accumulated amount A is given by

A=P(1+r)^t .......(1)

where, r is the rate of simple annual interest in decimal.

t is the time applied for interest.

For solving r divide both sides of equation by P in (1),we get

$\frac{A}{P}=(1+r)^t\\\Rightarrow(\frac{A}{P})^{\frac{1}{t}}=1+r\\\Rightarrow\ r=(\frac{A}{P})^{\frac{1}{t}}-1$ .

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