Question

How do you work out the rate, time and principal from the compound interest formula?
$A = P( {1 + \frac{r}{100} })^{n}$
​

Answer 1

Answer:

Part 1) $P=A/(1+\frac{r}{n})^{nt}$   (see the explanation)

Part 2) $r=n[\frac{A}{P}^{1/(nt)}-1]$    (see the explanation)

Part 3) $t=log(\frac{A}{P})/[(n)log(1+\frac{r}{n})]$   (see the explanation)

Step-by-step explanation:

we know that

The compound interest formula is equal to  

$A=P(1+\frac{r}{n})^{nt}$  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

Part 1) Find the Principal P

The values of A,r,n and t are given

Isolate the variable P

$A=P(1+\frac{r}{n})^{nt}$  

Divide both side by  $(1+\frac{r}{n})^{nt}$  

$P=A/(1+\frac{r}{n})^{nt}$  

Part 2) Find the rate r

The values of A,P,n and t are given

Isolate the variable r

$A=P(1+\frac{r}{n})^{nt}$  

Divide both sides by P

$\frac{A}{P} =(1+\frac{r}{n})^{nt}$  

Elevated both sides to 1/(nt)

$\frac{A}{P}^{1/(nt)} =(1+\frac{r}{n})$  

subtract 1 both sides

$\frac{A}{P}^{1/(nt)}-1 =\frac{r}{n}$  

Multiply by n both sides

$r=n[\frac{A}{P}^{1/(nt)}-1]$  

Part 3) Find the time t

The values of A,P,r and n are given

Isolate the variable t

$A=P(1+\frac{r}{n})^{nt}$  

Divide both sides by P

$\frac{A}{P} =(1+\frac{r}{n})^{nt}$  

Apply log both sides

$log(\frac{A}{P})=log(1+\frac{r}{n})^{nt}$  

Apply property of exponents

$log(\frac{A}{P})=(nt)log(1+\frac{r}{n})$  

Divide both side by $(n)log(1+\frac{r}{n})$  

$t=log(\frac{A}{P})/[(n)log(1+\frac{r}{n})]$