1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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})]  

You might be interested in
I'm not sure how to simplify this expression with the exponents rules of multiplication
Vedmedyk [2.9K]
The rule of exponential multiplication is (a^x)*(a^y)=a^(x+y)
using this with your expression, we can do
(10^1)*(10^3)*(10^2)=10^(1+3+2)=10^6
Final answer:
10^6 or 1 million
Hope I helped :)
3 0
3 years ago
To
yanalaym [24]

Answer:

I think it's 56 students have a gadgets

5 0
2 years ago
The price of a bicycle was decreased by 40% to £96. What was the price before the decrease?The price of a computer was decreased
Mkey [24]
The first one would be $160 and the second one would be $525
6 0
3 years ago
Help how many minutes does it take?
xxMikexx [17]

Answer:

7.8 minutes

Step-by-step explanation:

70 x 30 = 2,100

2,100 divided by 270 = 7.8 minutes.

4 0
2 years ago
Read 2 more answers
PLEASE HELP ITS DUE SOON!!!! 50 POINTS!!!!
Evgesh-ka [11]

Answer:

12xx^{5}

32n^3

x^2y^2

81a^4b^16

m^7/2

2p^5

2x^9

16n^13

2/n^2

8a^4/2x^5

x^2/4

1/b^11

4x^4

a^11

4m^3n^17

Step-by-step explanation:

Hope this helps!

(1-16 in order)

3 0
2 years ago
Read 2 more answers
Other questions:
  • Suppose you are using α = 0.05 to test the claim that μ > 23 using a p-value. you are given the sample statistics , and find
    7·1 answer
  • The height of the pyramid in the diagram is three times the radius of the cone. The base area of the pyramid is the same as the
    14·1 answer
  • Please help! I have a bunch more I will be posting as well , thank you! (:
    9·1 answer
  • Pls answer these McQ to be the brainliest
    7·1 answer
  • If 8p = 3p + 25, what is the value of p? Select the best answer from the choices provided. p = 4 p = 5 p = 6 p = 8
    7·2 answers
  • The number “Pi” (∏) is often rounded to what number?
    10·2 answers
  • The base of a rectangle prism is 20 cm. If the height of the prism is 5 cm what is it volume
    14·1 answer
  • Michiko bought pens for $3.85 and pencils for $1.25 how much did she spend all together? ​
    5·1 answer
  • Which shows 9.635 written in expanded form, using powers of ten
    15·1 answer
  • Anyone good at this??
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!