We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time period in years.
In this case, we are given that the principal (P) is Rs. 3750, the final amount (A) is Rs. 4374, the time period (t) is 2 years, and the interest is compounded annually (n = 1). We need to find the annual interest rate (r).
Substituting these values into the formula, we get:
4374 = 3750(1 + r/1)^(1*2)
Dividing both sides by 3750, we get:
1.1656 = (1 + r)^2
Taking the square root of both sides, we get:
1 + r = 1.0801
Subtracting 1 from both sides, we get:
r = 0.0801 = 8.01%
Therefore, the annual interest rate is 8.01%, and the sum of Rs. 3750 will amount to Rs. 4374 in 2 years if the interest is compounded annually at this rate.
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Verified answer
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)^(nt)
where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time period in years.
In this case, we are given that the principal (P) is Rs. 3750, the final amount (A) is Rs. 4374, the time period (t) is 2 years, and the interest is compounded annually (n = 1). We need to find the annual interest rate (r).
Substituting these values into the formula, we get:
4374 = 3750(1 + r/1)^(1*2)
Dividing both sides by 3750, we get:
1.1656 = (1 + r)^2
Taking the square root of both sides, we get:
1 + r = 1.0801
Subtracting 1 from both sides, we get:
r = 0.0801 = 8.01%
Therefore, the annual interest rate is 8.01%, and the sum of Rs. 3750 will amount to Rs. 4374 in 2 years if the interest is compounded annually at this rate.
The rate percent, if the interest is compounded annually, is 8%.
Given:
A sum of Rs. 3750 amounts to Rs. 4374 in 2 years.
To Find:
The rate percent if the interest is compounded annually.
Solution:
To find the rate percent if the interest is compounded annually, we will follow the following steps:
As we know the relation between principal amount, compound interest, rate, and time is given by:
[tex]s = p { (1 + \frac{r}{100}) }^{n} [/tex]
Here,
s is the sum after interest = Rs. 4374
p (the amount initially) = Rs. 3750
n = 2 years
Now,
In putting values we get,
[tex]4374 = 3750 {(1 + \frac{r}{100} )}^{2} [/tex]
[tex] \frac{4734}{3750} = {( 1 + \frac{r}{100}) }^{2} [/tex]
Taking square root on both sides we get,
[tex] \sqrt{\frac{4734}{3750} } = 1 + \frac{r}{100} [/tex]
[tex] \sqrt{ \frac{729}{625} } = 1 + \frac{r}{100} [/tex]
[tex] \frac{27}{25} = 1 + \frac{r}{100} [/tex]
[tex] \frac{27}{25} - 1 = \frac{r}{100} [/tex]
[tex] \frac{27 - 25}{27} = \frac{r}{100} [/tex]
[tex] \frac{2}{25} \times 100 = r[/tex]
[tex]r = 4 \times 2 = 8\%[/tex]
Henceforth, the rate percent, if the interest is compounded annually, is 8%.
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