In what time will ₹1500 yield ₹496.50 as compound Interest at 10% per annum compounded annually
Answers
Step-by-step explanation:
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Answer:
1500 yields 496.50 as compound interest at 10% per annum compounded annually.
To find:
The time period
Solution:
To solve the given problem we will use the following formula:
\boxed{\bold{C.I. = P [(1 + \frac{R}{100})^n - 1]}}
C.I.=P[(1+
100
R
)
n
−1]
where
P = principal
R = rate of interest
n = time period
Now, we will substitute C.I. = Rs. 496.50, P = Rs. 1500 and R = 10% in the above formula:
496.50 = 1500[(1+ \frac{10}{100})^n - 1]496.50=1500[(1+
100
10
)
n
−1]
\implies \frac{496.50}{1500} = [(1+ \frac{10}{100})^n - 1]⟹
1500
496.50
=[(1+
100
10
)
n
−1]
\implies \frac{49650}{150000} = [( \frac{110}{100})^n - 1]⟹
150000
49650
=[(
100
110
)
n
−1]
\implies 0.331 = [( \frac{110}{100})^n - 1]⟹0.331=[(
100
110
)
n
−1]
\implies 0.331 + 1 = ( \frac{11}{10})^n⟹0.331+1=(
10
11
)
n
\implies 1.331 = ( \frac{11}{10})^n⟹1.331=(
10
11
)
n
\implies \frac{1331}{1000} = ( \frac{11}{10})^n⟹
1000
1331
=(
10
11
)
n
\implies (\frac{11}{10})^3 = ( \frac{11}{10})^n⟹(
10
11
)
3
=(
10
11
)
n
\implies \bold{n = 3 \:years}⟹n=3years
Thus, in 3 years Rs. 1500 will yield Rs. 496.50 as compound interest at 10% p.a. compounded annually.
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