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Stels [109]
3 years ago
15

How do you work out the rate, time and principal from the compound interest formula?

Mathematics
1 answer:
wlad13 [49]3 years ago
3 0

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})]  

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