Compound Interest
- Rs. 16,820 is divided between two brothers of age 27 years and 25 years. They invested their money at 5% per annum compound interest in such a way that both will receive equal money at the age of 40 years. The share (in Rs.) of elder brother is
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Suppose Share of elder brother = Rs. y
∴ Share of younger brother = Rs. (16820 – y)
Using the given formula ,A = P 
1 + R 
T 100
According to the question,y 1 + 5 13 = (16820 – y) 1 + 5 15 100 100 ⇒ y = (16820 – y) 1 + 1 2 20 ⇒ y = (16820 – y) 21 2 20 ⇒ y = (16820 – y) 21 2 20
Correct Option: C
Suppose Share of elder brother = Rs. y
∴ Share of younger brother = Rs. (16820 – y)
Using the given formula ,A = P 1 + R T 100
According to the question,y 1 + 5 13 = (16820 – y) 1 + 5 15 100 100 ⇒ y = (16820 – y) 1 + 1 2 20 ⇒ y = (16820 – y) 21 2 20 ⇒ y = (16820 – y) 21 2 20 ⇒ 21 2 y = 16820 – y 20 ⇒ 400y + y = 16820 441 ⇒ 400y + 441y = 16820 441
⇒ 841y = 16820 × 441⇒ y = 16820 × 441 = Rs. 8820 841
- A sum of ₹ 210 was taken as a loan. This is to be paid back in two equal instalments. If the rate of interest be 10% compounded annually, then the value of each instalment is
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Here , Loan = ₹ 210 , R = 10%
Let the value of each instalment be ₹ y
∴ Principal = Present worth of₹ y due 1 year hence, present worth of Rs. y due 2 years hence⇒ 210 = y + y 1 + R 
1 + R 2 100 100 ⇒ 210 = y + y 1 + 10 1 + 10 2 100 100 ⇒ 210 = y + y 1 + 1 1 + 1 2 10 10 ⇒ 210 = y + y 11 11 2 10 10
Correct Option: B
Here , Loan = ₹ 210 , R = 10%
Let the value of each instalment be ₹ y
∴ Principal = Present worth of₹ y due 1 year hence, present worth of Rs. y due 2 years hence⇒ 210 = y + y 1 + R 1 + R 2 100 100 ⇒ 210 = y + y 1 + 10 1 + 10 2 100 100 ⇒ 210 = y + y 1 + 1 1 + 1 2 10 10 ⇒ 210 = y + y 11 11 2 10 10 ⇒ 210 = 10y + 100y 11 121 ⇒ 210 = 110y + 100y 121
⇒ 210 × 121 = 210 y⇒ y = 210 × 121 = ₹ 121 210
- A loan of ₹ 12,300 at 5% per annum compound interest, is to be repaid in two equal annual
instalments at the end of every year. Find the amount of each instalment.
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Given that , Loan = ₹ 12,300 , r = 5% per annum
Let each instalment be y.∴ y + y = 12300 1 + 5 1 + 5 2 100 100 ⇒ 20y + 20 2 y = 12300 21 21 ⇒ 20y 1 + 20 = 12300 21 21
Correct Option: B
Given that , Loan = ₹ 12,300 , r = 5% per annum
Let each instalment be y.∴ y + y = 12300 1 + 5 1 + 5 2 100 100 ⇒ 20y + 20 2 y = 12300 21 21 ⇒ 20y 1 + 20 = 12300 21 21 ⇒ 20y × 41 × y = 12300 21 21 ⇒ y = 12300 × 21 × 21 = ₹ 6615 20 × 41
- Find the effective annual rate of 5 per cent per annum compound interest paid half yearly ?
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The amount of Rs. 100 in one year at compound interest at 5% per annum payable half yearly.
= Rs. 100(1 + 5/2 /100)2Correct Option: C
The amount of Rs. 100 in one year at compound interest at 5% per annum payable half yearly.
= Rs. 100(1 + 5/2 /100)2
=Rs. 100(102.5/100)2
=Rs. 100(1.025)2
=Rs. 105.0625
Thus, the nominal rate of 5% payable half yearly has the same effect as the rate of 5.0625 per cent would have, if payable yearly.
Hence 5.0625 per cent is called the effective annual rate 5% per annum payable half yearly.
- If the compound interest on a certain sum for 2 years at 12.5% per annum is 170, the simple interest is ?
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Let the principle is P
so compound interest = p x ( 1 + (12.5/100))sup>2 - p = 170
⇒ p x (112.5/100) x (112.5/100) - p = 170
⇒ P [ 12656.25 - 10000 ] = 170 x 10000
∴ p = (170 x 10000) / 2656.25
Simple interest SI = (P x T x R )/100
= [{(170 x 10000) / 2656.25} x 2 x 12.5] / 100
= 160
Correct Option: C
Let the principle is P
so compound interest = p x ( 1 + (12.5/100))sup>2 - p = 170
⇒ p x (112.5/100) x (112.5/100) - p = 170
⇒ P [ 12656.25 - 10000 ] = 170 x 10000
∴ p = (170 x 10000) / 2656.25
Simple interest SI = (P x T x R )/100
= [{(170 x 10000) / 2656.25} x 2 x 12.5] / 100
= 160
