Money invested in compound interest amount to rs 27783 in 3 years and rs 26460 in 2 years what is the rate percent of interest ?
26460= P (1+r)^2
27783 = P (1+r)^3
P = 26460/(1+r)^2
27783 = [26460/(1+r)^2] (1+r)^3
(1+r) = 27783/26460
(1+r) = 1.05
5%
To find the rate percent of interest, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount
P = Principal amount
r = Annual interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
We have two scenarios:
Scenario 1:
A = Rs 27,783
P = Principal amount (unknown)
r = Annual interest rate (unknown)
n = Number of times the interest is compounded per year (unknown)
t = 3 years
Scenario 2:
A = Rs 26,460
P = Principal amount (unknown)
r = Annual interest rate (unknown)
n = Number of times the interest is compounded per year (unknown)
t = 2 years
We can set up two equations using these scenarios:
Scenario 1: 27783 = P(1 + r/n)^(3n)
Scenario 2: 26460 = P(1 + r/n)^(2n)
Solving these equations will give us the values of P, r, and n, which will allow us to calculate the rate percent of interest.
Unfortunately, without additional information or more equations, we cannot solve for the rate percent of interest.
To determine the rate of interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the amount after compound interest
P is the principal amount (initial investment)
r is the annual interest rate (in decimal form)
n is the number of compounding periods per year
t is the number of years
Let's solve this step by step:
1. Calculate the compound interest for the first scenario:
Given that Rs 27,783 is the final amount after 3 years, we can assume that this is equal to A (i.e., A = 27783).
Step 1: Substitute the values in the formula:
27783 = P(1 + r/n)^(nt)
2. Calculate the compound interest for the second scenario:
Given that Rs 26,460 is the final amount after 2 years, we can assume that this is equal to A (i.e., A = 26460).
Step 2: Substitute the values in the formula:
26460 = P(1 + r/n)^(nt)
Now we have two equations with two unknowns (P and r).
3. Find the ratio of the two equations:
Divide the second equation by the first equation to eliminate P:
26460/27783 = [P(1 + r/n)^(nt)]/[P(1 + r/n)^(nt)]
0.9516 = (1 + r/n)^(nt) / (1 + r/n)^(3nt)
4. Simplify the equation and solve for (1 + r/n)^(nt):
0.9516 = (1 + r/n)^(2nt) / (1 + r/n)^(3nt)
5. Take the square root of both sides to remove the exponent from (1 + r/n)^(2nt):
√(0.9516) = 1 + r/n
6. Subtract 1 from both sides:
√(0.9516) - 1 = r/n
7. Multiply both sides by n:
n * (√(0.9516) - 1) = r
Now we have the value of r (rate of interest) in terms of n. However, since we do not have the value of n, we cannot find the exact interest rate. To calculate the interest rate, we need additional information such as the number of compounding periods per year (n).