Rs. 4,000 is given at 5% per annum for one year and interest is compounded half yearly, Rs. 2,000 is given at 40% per annum compounded quarterly for 1 year. The total interest received is nearest to:
- Rs. 1,130.70
- Rs. 1,333.30
- Rs. 1,444.40
- Rs. 1,888.80
Answer (Detailed Solution Below)
Option 1 : Rs. 1,130.70
Free
Electric charges and coulomb's law (Basic)
10 Questions 10 Marks 10 Mins
Equivalent rate of interest for one year = 2.5 + 2.5 + (2.5 × 2.5)/100
⇒ 5.0625%
Compound interest = 4000 × 5.0625/100 = Rs. 202.5
Rate of interest quarterly = 40/4 = 10%
Equivalent rate of interest = [(11/10 × 11/10 × 11/10 × 11/10) - 1] = 46.41%
Compound interest = 2000 × 46.41/100 = Rs. 928.2
Total interest = 202.5 + 928.2 = Rs. 1130.70
Traditional method:
Given
Case-1
Principal = Rs. 4000
Rate = 5%
Time = 1 year
Interest compounded half yearly.
Case-2
Principal = Rs. 2000
Rate = 40%
Time = 1 year
Interest compounded quaterly.
Formula:
A = P (1 + r/100)t
Calculation:
For case-1
r = 5/2% = 2.5%
Time = 2
According to the formula
A = 4000 × (102.5/100) × (102.5/100)
⇒ A = 4,202.5
CI = 4,202,5 - 4,000 = 202.5
For case-2
r = 40/4 = 10%
Time = 4
According to the formula
A = 2000 × (110/100) × (110/100) × (110/100) × (110/100)
⇒ A = 2,928.2
CI = 2,928.2 - 2,000 = Rs. 928.2
Total interest = 202.5 + 928.2 = Rs. 1,130.70
∴ The total interest is Rs. 1,130.70.
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Let's discuss the concepts related to Interest and Compound Interest. Explore more from Quantitative Aptitude here. Learn now!
At what rate per annum will Rs. 40000 yield a compound interest of Rs. 6305 in 9 months, if the interest is being compounded quarterly?
- 20%
- 32%
- 50%
- 80%
Answer (Detailed Solution Below)
Option 1 : 20%
Free
ME Subject Test 1: Strength of Materials
20 Questions 20 Marks 18 Mins
GIVEN:
Principal = Rs. 40000
Compound Interest = Rs. 6305
Time = 9 months
FORMULA USED:
CI = P [ (1 + R/100)ᵀ – 1]
CALCULATION:
Let the rate of C.I be R per cent per annum.
∴ CI = P [ (1 + R/100)ᵀ – 1]
⇒ 6305 = 40000 [ (1 + R/400)3 – 1 ] [T = 9 × 4 = 36 months = 3 years because interest is calculated quarterly]
⇒ 6305/40000 = (1 + R/400)3 – 1
⇒ (1 + R/400)3 – 1 = 1,261/8,000
⇒ (1 + R/400)3 = 1 + 1,261/8,000
⇒ (1 + R/400)3 = 9,261/8,000
⇒ (1 + R/400)3 = (21/20)3
⇒ 1 + R/400 = 21/20
⇒ R/400 = 21/20 – 1 = 1/20
∴ rate = R = 400/20 = 20%
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