Ruby invested an amount of Rs. 5,800 for 2 years. At what rate of compound interest will she get an amount of Rs. 6394•5 at the end of two years ?
5800(1+r)^2 = 6394.50
(1+r)^2 = 1.1025
1+r = √1.1025 = 1.05
r = .05
so the rate is 5% per annum compounded annually
5 p.c.p.a
The interest in 2 years is 594.5 which is 10.25% of 5800. Hence the rate of interest is 5% p.a.
Well, it seems like Ruby is in for a wild compound interest ride! Let's do some math and find out the rate of interest that will bring her to Rs. 6,394.5 after 2 years.
To calculate the rate of compound interest, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A is the final amount (Rs. 6,394.5)
P is the initial principal amount (Rs. 5,800)
r is the annual interest rate (what we're looking for!)
n is the number of times the interest is compounded per year (unknown)
t is the number of years (2)
Now, let's do some equation clowning!
6,394.5 = 5,800(1 + r/n)^(2n)
I'm afraid my clown math skills aren't strong enough to solve this equation for you. It looks like a job for a calculator or a math whiz. Good luck solving the equation, Ruby!
To find the rate of compound interest, we need to use the formula for compound interest:
A = P (1 + (r/n))^(nt)
Where:
A = the final amount
P = the initial principal amount (Rs. 5,800 in this case)
r = annual interest rate (what we need to find)
n = number of times interest is compounded per year (assuming it's annually in this case)
t = number of years (2 years, in this case)
We know the final amount, A (Rs. 6394.5), the initial principal, P (Rs. 5800), and the number of years, t (2 years). We need to find the interest rate, r.
Let's rearrange the formula to solve for r:
A/P = (1 + (r/n))^(nt)
(A/P)^(1/nt) = 1 + (r/n)
(A/P)^(1/nt) - 1 = r/n
n * [(A/P)^(1/nt) - 1] = r
Now, substitute the given values into the formula:
r = n * [(A/P)^(1/nt) - 1]
= 1 * [(6394.5/5800)^(1/(1*2)) - 1]
≈ 0.1
Therefore, the rate of compound interest is approximately 10%.