Solution:
For Simple Interest:
A = (P × R × T)/100
P = ₹ 12,000
T = 2 years
R = 6% simple interest
where , A = Amount, P = Principal, T = Time period in years and R = Rate percent\
Simple Interest to be paid for 2 years at the rate of 6% per annum
S.I. for 2 years = 2 × 12000 × (6/100)
= 2 × 120 × 6
= 1440
For Compound Interest:
A = P[1 + (r/100)]n
P = ₹ 12,000
n = 2 years
R = 6% compounded annually
Compound Interest to be paid for 2 years at the rate of 6% per annum
A = P[1 + (r/100)]n
A = 12000[1 + (6/100)]2
A = 12000[(100/100) + (6/100)]2
A = 12000 × (106/100) × (106/100)
A = 12000 × (11236/10000)
A = 12000 × 1.1236
A = 13483.20
Compound Interest = A - P
= 13483.20 - 12000
= ₹ 1483.20
Compound Interest - Simple Interest = 1483.20 - 1440
= ₹ 43.20
☛ Check: NCERT Solutions for Class 8 Maths Chapter 8
Video Solution:
NCERT Solutions Class 8 Maths Chapter 8 Exercise 8.3 Question 4
Summary:
I borrowed ₹ 12,000 from Jamshed at 6% per annum simple interest for 2 years. Had I borrowed this sum at 6% per annum compound interest, the extra amount I would have to pay ₹ 43.20.
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Given:
The sum = Rs 12,000
Time = \(1 \frac{1}{2}\) years
Rate = 10% p.a.
Formula used:
A = P(1 + R/100)t
Here, A, P, R and t are the Amount, Principal, Rate and time respectively
Concept used:
When compounded half-yearly then,
Rate is half and time is doubled
Calculation:
Rate = 10%/2 = 5% and Time = \(1 \frac{1}{2}\) × 2 = 3 half yearly
Now, A = P(1 + R/100)t
⇒ A = 12000(1 + 5/100)3
⇒ A = 12000 × 21/20 × 21/20 × 21/20
⇒ A = 13891.5
∴ The total amounts to be paid is Rs 13891.50
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Last updated at Nov. 12, 2018 by Teachoo
Example 12 What amount is to be repaid on a loan of Rs 12000 for 1 1/2 years at 10% per annum compounded half yearly. Given Principal = Rs 12000 Here, rate is compounded half yearly. Rate of interest = R = 10/2 % = 5 % & Time = 1 1/2 years = 3/2 years = 3/2 × 2 half years = 3 Amount = P (1+𝑅/100)^𝑛 = 12000 (1+5/100)^3 = 12000 (1+1/20)^3 = 12000 ((20 + 1)/20)^3 = 12000 (21/20)^3 = 12000 × 21/20 × 21/20 × 21/20 = 12 × 21/2 × 21/2 × 21/2 = 3 × 21 × 21 × 21/2 = (63 × 441)/2 = 27783/2 = 13891.5 ∴ Amount = Rs 13,891.50
Next: Example 13 Important →
Text Solution
Solution : Here, interest is compounded half-yearly.So, <br> Time, `t = 3` half years<br> `:.`Rate of interest `r = 10/2 = 5% ` per half yearly<br> Loan amount, `P = "Rs." 12000` <br> So, Amount to be repaid, `A = 12000(1+5/100)^3`<br> `A = 12000xx(21/20)xx(21/20)xx(21/20) = "Rs."13891.5`