A sum is invested at compound interest payable annually. The interest in two successive years was Rs 900 and Rs 981. Find the sum.

If the sum of all internal angles and sum of all external angles of a regular polygon are equal, then the number of sides of the polygon is?
Pls help***

let the amount invested be P

let the rate be i

900 must be the difference in the balance between year n and year n+1, and the same for the following year:
p(1+i)^(n+1) - p(1+i)^n = 900
p(1+i)^(n+2) - p^(n+1)^(n+1) = 981

from first: p(1+i)^n[(1+i - 1) = 900
from 2nd: p(1+i)^n[ (1+i)2 - (1+i)] = 981
divide them:
i/(1 + 2i + i^2 -1 - i) = 100/109
100i^2 + 100i = 109i
100i^2 -9i = 0
i(100i - 9) = 0
i = 0 , not likely or i = 9/100 = .09 or 9%

so what amount would yield $900 at 9% ?
= 900/.09 = $10,000

I believe I was overthinking that question.

#2
suppose we have an n-gon
sum of interior angles = 180(n-2)
sum of all the exterior angles of any n-gon = 360°
so
180(n-2) = 360
n-2 = 2
n = 4

must be a quadrilateral

To find the sum invested, we need to use the compound interest formula:

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

Where:
A = the final amount after interest
P = the principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = time in years

Let's use the given information to solve the problem.

First, we need to find the values of r, t, and n:

For the first year, the interest is Rs 900. Let's denote it as I1.
For the second year, the interest is Rs 981. Let's denote it as I2.

We know that:
I1 = P(1 + r/n)^(n*1)
I2 = P(1 + r/n)^(n*2)

Dividing the two equations, we get:

I2/I1 = [(1 + r/n)^(n*2)] / [(1 + r/n)^(n*1)]

Simplifying, we have:

I2/I1 = (1 + r/n)^(n*2 - n*1)
I2/I1 = (1 + r/n)^n
(I2/I1)^(1/n) = 1 + r/n
(I2/I1)^(1/n) - 1 = r/n

Now, we can substitute the values of I1 and I2:

(I2/I1)^(1/n) - 1 = r/n
(981/900)^(1/n) - 1 = r/n

Let's assume a value for n, say n = 2. We can then solve for r:

(981/900)^(1/2) - 1 = r/2

We can use this equation to find the value of r. Once we have r, we can use it to find the value of P by rearranging the compound interest formula:

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

Substituting the values of A, r, n, and t, we can calculate the sum invested.

Regarding the second question about the regular polygon, the sum of all internal angles of a polygon with n sides can be calculated using the formula:

Sum of interior angles = (n - 2) * 180 degrees

The sum of all external angles in any polygon is always 360 degrees.

Since the question states that the sum of all internal angles is equal to the sum of all external angles, we can set up the following equation:

(n - 2) * 180 = 360

Solving this equation will give us the value of n, which represents the number of sides of the polygon.