find the amount on a sum of ₹2000 for two years when the interest is compund annually at 10% per annum
Answers
Answer:
Rs 420
Step-by-step explanation:
⇒ A=P(1+
100
R
)
T
⇒ A=2000×(1+
100
10
)
2
⇒ A=2000×
100
121
⇒ A=Rs.2420.
∴ C.I.=A−P=Rs.2420−Rs.2000=Rs.420.
Answer:
Given:
A sum of Rs. 2000 at 10% pa for two and a half years, compounded annually
To find:
The amount and compound interest
Solution:
We will use the following of compound interest for 2 and a half years to solve the given problem:
A = P [1 + \frac{R}{100} ]^2[1 + \frac{\frac{R}{2}}{100} ]A=P[1+
100
R
]
2
[1+
100
2
R
]
C.I. = A - PC.I.=A−P
Here we have,
The sum of money, P = Rs. 2000
The rate of interest, R = 10%
Time period, n = 2\frac{1}{2} \:years2
2
1
years
∴ A = 2000 [1 + \frac{10}{100} ]^2[1 + \frac{\frac{10}{2} }{100} ]A=2000[1+
100
10
]
2
[1+
100
2
10
]
\implies A = 2000 [\frac{110}{100} ]^2[1 + \frac{5 }{100} ]⟹A=2000[
100
110
]
2
[1+
100
5
]
\implies A = 2000 [\frac{110}{100} ]^2[ \frac{105 }{100} ]⟹A=2000[
100
110
]
2
[
100
105
]
\implies A = 2000 [1.1 ]^2[1.05 ]⟹A=2000[1.1]
2
[1.05]
\implies A = 2000 [1.21 ][1.05 ]⟹A=2000[1.21][1.05]
\implies \bold{A = 2541}⟹A=2541 ← the amount
∴ C.I. = A - P = Rs. 2541 - Rs. 2000 = \bold{Rs. 541}C.I.=A−P=Rs.2541−Rs.2000=Rs.541
Thus, the amount is Rs. 2541 and the compound interest is Rs. 541.
Step-by-step explanation: