find the compound interest of principal=rs 12,550, amount=?, rate of interest=9% semi annually, time= 2.5
12550(1.045)^5 - 1)
A=p(1+r)^t=800(1+0.08)3
To find the compound interest, we need to use the formula:
A = P(1 + r/n)^(nt)
Where:
A = Amount after compound interest
P = Principal
r = Rate of interest (in decimal form)
n = Number of times interest is compounded per time period
t = Time period
Given:
Principal (P) = Rs 12,550
Rate of interest (r) = 9% (9/100 = 0.09)
Time period (t) = 2.5 years
Interest compounded semi-annually (n = 2)
Let's substitute these values into the formula:
A = 12550(1 + 0.09/2)^(2*2.5)
A = 12550(1 + 0.045)^(5)
A = 12550(1.045)^5
A = 12550(1.22965)
A ≈ Rs 15,530.51
Therefore, the amount after compound interest is approximately Rs 15,530.51.
To find the compound interest, we first need to determine the amount. The formula to calculate the compound amount is:
Amount = Principal * (1 + (Rate/100))^Time
Given:
Principal (P) = Rs 12,550
Rate of Interest (R) = 9% per annum (semi-annually compounded)
Time (T) = 2.5 years
Dividing the Rate of Interest by 2 (as it is compounded semi-annually), we get an effective rate of 4.5% per semi-annual period.
Now, we can substitute the values into the formula to calculate the amount:
Amount = Rs 12,550 * (1 + (4.5/100))^2.5
Before solving this equation, let's break it down into steps.
Step 1: Calculate the rate per semi-annual period.
Rate per semi-annual period = Rate/2 = 9%/2 = 4.5%
Step 2: Calculate the compound amount.
Amount = Principal * (1 + Rate per semi-annual period/100)^Time
Now, let's substitute the values:
Amount = Rs 12,550 * (1 + 4.5/100)^2.5
Calculating the expression inside the brackets:
(1 + 4.5/100) = (1 + 0.045) = 1.045
Calculating the compound amount:
Amount = Rs 12,550 * 1.045^2.5
Now, let's solve this using a calculator:
Amount = Rs 12,550 * 1.104497365
Amount ≈ Rs 13,866.52
Therefore, the compound interest is approximately Rs 13,866.52 - Rs 12,550 = Rs 1,316.52.