what will be the compound interest at the rate of 10% per annum for 3 years on a principal amounts which in 3 years gives Rs 1200 as the simple interest at yhe rate of 4% per annum ?
ans = Rs 3310.
Answers
Answer:
Time (n)=3 years
Rate (r)=10%
CI = Rs. 993
Let sum be P.
C.I. =P×[(1+
100
r
)
n
−1]
⇒993=P×
⎣
⎢
⎡
(1+
100
10
)
3
−1
⎦
⎥
⎤
993=P×
⎣
⎢
⎡
(
10
11
)
3
−1
⎦
⎥
⎤
⇒993=p(1.331−1)
⇒0.331P=993
⇒P=3000
Now, Simple Interest,
S.I. =
100
PTR
S.I. =
100
3000×3×10
= Rs. 900
Step-by-step explanation:
To find the compound interest at the rate of 10% per annum for 3 years on a principal amount that in 3 years gives Rs 1200 as the simple interest at the rate of 4% per annum, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the compound interest
P = the principal amount
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the number of years
Given that:
r1 = 0.04 (the annual interest rate for simple interest)
r2 = 0.10 (the annual interest rate for compound interest)
n = 1 (assuming interest is compounded annually)
t = 3
We know that the simple interest in 3 years is Rs 1200, so we can use the formula for simple interest to find the principal amount:
I = Prt
Where:
I = the simple interest
P = the principal amount
r = the annual interest rate (expressed as a decimal)
t = the number of years
Given:
I = 1200
r = 0.04
t = 3
So we can find P as:
P = I/rt = 1200/(0.04*3) = 1200/0.12 = 10000
Now that we have the principal amount, we can use the formula for compound interest to find the compound interest:
A = P(1 + r/n)^(nt)
Given:
P= 10000
r = 0.10
n = 1
t = 3
A = 10000(1 + 0.10)^3 = 10000(1.331) = 13310
So, the compound interest at the rate of 10% per annum for 3 years on a principal amount that in 3 years gives Rs 1200 as the simple interest at the rate of 4% per annum is Rs 13310.
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