The document RD Sharma Solutions - Chapter 14 - Compound Interest (Part - 2), Class 8, Maths Class 8 Notes | EduRev is a part of the Class 8 Course RD Sharma Solutions for Class 8 Mathematics.

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**PAGE NO 14.14:**

**Question 1:**

**Compute the amount and the compound interest in each of the following by using the formulae when: (i) Principal = Rs 3000, Rate = 5%, Time = 2 years (ii) Principal = Rs 3000, Rate = 18%, Time = 2 years (iii) Principal = Rs 5000, Rate = 10 paise per rupee per annum, Time = 2 years (iv) Principal = Rs 2000, Rate = 4 paise per rupee per annum, Time = 3 years (v) Principal = Rs 12800, Rate = 7(1/2)%, Time = 3 years (vi) Principal = Rs 10000, Rate 20% per annum compounded half-yearly, Time = 2 years (vii) Principal = Rs 160000, Rate = 10 paise per rupee per annum compounded half-yearly, Time = 2 years.**

**ANSWER:**

Applying the rule A = P(1 + R/100)^{n} on the given situations, we get:

(i)A = 3,000(1 + 5/100)Â²

= 3,000(1.05)Â²

= Rs 3,307.50

Now,CI = A âˆ’ P

= Rs 3,307.50 âˆ’ Rs 3,000

= Rs 307.50

(ii)A = 3,000(1 + 18/100)Â²

= 3,000(1.18)Â²

= Rs 4,177.20

Now,CI = A âˆ’ P

= Rs 4,177.20 âˆ’ Rs 3,000

= Rs 1,177.20

(iii)A = 5,000(1 + 10/100)Â²

= 5,000(1.10)Â²

= Rs 6,050

Now,CI = A âˆ’ P

= Rs 6,050 âˆ’ Rs 5,000

= Rs 1,050

(iv)A = 2,000(1 + 4/100)Â³

= 2,000(1.04)Â³

= Rs 2,249.68

Now,CI = A âˆ’ P

= Rs 2,249.68 âˆ’ Rs 2,000

= Rs 249.68

(v)A = 12,800(1 + 7.5/100)Â³

= 12,800(1.075)Â³

= Rs 15,901.40

Now,CI = A âˆ’ P

= Rs 15,901.40 âˆ’ Rs 12,800

= Rs 3,101.40

(vi)A = 10,000(1 + 20/200)^{4}

= 10,000(1.1)^{4 }

= Rs 14,641

Now,CI = A âˆ’ P

= Rs 14,641 âˆ’ Rs 10,000

= Rs 4,641

(vii)A = 16,000(1 + 10/200)^{4}

= 16,000(1.05)^{4}

= Rs 19,448.1

Now,CI = A âˆ’ P

= Rs 19,448.1 âˆ’ Rs 16,000

= Rs 3,448.1

**PAGE NO 14.14:**

**Question 2:**

**Find the amount of Rs 2400 after 3 years, when the interest is compounded annually at the rate of 20% per annum.**

**ANSWER:**

Given: P = Rs 2,400

R = 20% p.a.

n = 3 years

We know that amount A at the end of n years at the rate R% per annum when the interest is compounded annually is given by

A = P(1 + R/100)^{n}

âˆ´ A = 2,400(1 + 20100)Â³

= 2,400(1.2)Â³

= 4,147.20

Thus, the required amount is Rs 4,147.20.

**PAGE NO 14.14:**

**Question 3:**

**Rahman lent Rs 16000 to Rasheed at the rate of 12.5% per annum compound interest. Find the amount payable by Rasheed to Rahman after 3 years.**

**ANSWER:**

Given: P = Rs 16,000

R = 12.5% p.a.

n = 3 years

We know that amount A at the end of n years at the rate R% per annum when the interest is compounded annually is given by

A = P(1 + R/100)^{n}.

âˆ´ A = 16,000(1 + 12.5/100)Â³

= 16,000(1.125)Â³

= 22,781.25

Thus, the required amount is Rs 22,781.25.

**PAGE NO 14.14:**

**Question 4:**

**Meera borrowed a sum of Rs 1000 from Sita for two years. If the rate of interest is 10% compounded annually, find the amount that Meera has to pay back.**

**ANSWER:**

Given: P = Rs 1,000

R = 10% p.a.

n = 2 years

We know that amount A at the end of n years at the rate R% per annum when the interest is compounded annually is given by

A = P(1 + R/100).

âˆ´ A = 1,000(1 + 10/100)Â²

= 1,000(1.1)Â² = 1,210

Thus, the required amount is Rs 1,210.

**PAGE NO 14.14:**

**Question 5:**

**Find the difference between the compound interest and simple interest. On a sum of Rs 50,000 at 10% per annum for 2 years.**

**ANSWER:**

Given: P = Rs 50,000

R = 10% p.a.

n = 2 years

A = P(1 + R/100)

.âˆ´ A = Rs 50,000(1 + 10/100)Â²

= Rs 50,000(1.1)Â²

= Rs 60,500

Also,CI = A âˆ’ P

= Rs 60,500 âˆ’ Rs 50,000

= Rs 10,500

We know that:

âˆ´ Difference between CI and SI = Rs 10,500 âˆ’ Rs 10,000

= Rs 500

**PAGE NO 14.15:**

**Question 6:**

**Amit borrowed Rs 16000 at 17.5% per annum simple interest. On the same day, he lent it to Ashu at the same rate but compounded annually. What does he gain at the end of 2 years?**

**ANSWER:**

Amount to be paid by Amit:

= Rs 5,600

Amount gained by Amit:A = P(1 + R/100)^{n }

= Rs 16,000(1 + 17.5/100)Â²

= Rs 16,000(1.175)Â²

= Rs 22,090

We know that:CI = A âˆ’ P

= Rs 22,090 âˆ’ Rs 16,000 = Rs 6090

Amit's gain in the whole transaction = Rs 6,090 âˆ’ Rs 5,600

= Rs 490

**PAGE NO 14.15:**

**Question 7:**

**Find the amount of Rs 4096 for 18 months at 12.5% per annum, the interest being compounded semi-annually.**

**ANSWER:**

Given:P = Rs 4,096

R = 12.5% p.a.

n = 18 months = 1.5 years

We have:A = P(1 + R/100)^{n}

When the interest is compounded semi âˆ’ annually, we have:

A = P(1 + R/200)Â²^{n }

= Rs 4,096(1 + 12.5/200)Â³

= Rs 4,096(1.0625)Â³

= Rs 4,913

Thus, the required amount is Rs 4,913.

**PAGE NO 14.15:**

**Question 8:**

**Find the amount and the compound interest on Rs 8000 for 1.5 years at 10% per annum, compounded half-yearly.**

**ANSWER:**

Given: P = Rs 8,000

R = 10% p.a.

n = 1.5 years

When compounded half âˆ’ yearly, we have:

A = P(1 + R/200)Â²^{n }

= Rs 8,000(1 + 10/200)Â³

= Rs 8,000(1.05)Â³

= Rs 9,261

Also,CI = A âˆ’ P

= Rs 9,261 âˆ’ Rs 8,000

= Rs 1,261

**PAGE NO 14.15:**

**Question 9:**

**Kamal borrowed Rs 57600 from LIC against her policy at 12.5% per annum to build a house. Find the amount that she pays to the LIC after 1.5 years if the interest is calculated half-yearly.**

**ANSWER:**

Given: P = Rs 57,600

R = 12.5% p.a.

n = 1.5 years

When the interest is compounded half âˆ’ yearly, we have:

A = P(1 + R/200)Â²n

= Rs 57,600(1 + 12.5/200)Â³

= Rs 57,600(1.0625)Â³

= Rs 69,089.06

Thus, the required amount is Rs 69,089.06.

**PAGE NO 14.15:**

**Question 10:**

**Abha purchased a house from Avas Parishad on credit. If the cost of the house is Rs 64000 and the rate of interest is 5% per annum compounded half-yearly, find the interest paid by Abha after one year and a half.**

**ANSWER:**

Given:P = Rs 64,000

R = 5% p.a.

n = 1.5 years

When the interest is compounded half âˆ’ yearly, we have:

A = P(1 + R/200)Â²^{n}

= Rs 64,000(1 + 5/200)Â³

= Rs 64,000(1.025)Â³

= Rs 68,921

Also,CI = A âˆ’ P

= Rs 68,921 âˆ’ Rs 64,000

= Rs 4,921

Thus, the required interest is Rs 4,921.

**PAGE NO 14.15:**

**Question 11:**

**Rakesh lent out Rs 10000 for 2 years at 20% per annum, compounded annually. How much more he could earn if the interest be compounded half-yearly?**

**ANSWER:**

Given:P = Rs 10,000

R = 20% p.a.

n = 2 years

A = P(1 + R/100)^{n}

= Rs 10,000(1 + 20/100)Â²

= Rs 10,000(1.2)Â²

= Rs 14,400

When the interest is compounded half âˆ’ yearly, we have:A = P(1 + R/200)Â²^{n }

= Rs 10,000(1 + 20/200)^{4 }

= Rs 10,000(1.1)^{4}

= Rs 14,641

Difference = Rs 14,641 âˆ’ Rs 14,400

= Rs 241

**PAGE NO 14.15:**

**Question 12:**

**Romesh borrowed a sum of Rs 245760 at 12.5% per annum, compounded annually. On the same day, he lent out his money to Ramu at the same rate of interest, but compounded semi-annually. Find his gain after 2 years.**

**ANSWER:**

Given: P = Rs 245,760

R = 12.5% p.a.

n = 2 years

When compounded annually, we have:A = P(1 + R/100)^{n }

= Rs 245,760(1 + 12.5/100)Â²

= Rs 311,040

When compounded semi âˆ’ annually,

we have:A = P(1 + R/200)Â²^{n}

= Rs 245,760(1 + 12.5/200)^{4}

= Rs 245,760(1.0625)^{4 }

= Rs 313,203.75

Romesh's gain = Rs 313,203.75 âˆ’ Rs 311,040

= Rs 2,163.75

**PAGE NO 14.15:**

**Question 13:**

**Find the amount that David would receive if he invests Rs 8192 for 18 months at 12.5% per annum, the interest being compounded half-yearly.**

**ANSWER:**

Given:P = Rs 8,192

R = 12.5% p.a.

n = 1.5 years

When the interest is compounded half âˆ’ yearly, we have:A = P(1 + R/200)^{Â²n}

= Rs 8,192(1 + 12.5/200)Â³

= Rs 8,192(1.0625)Â³

= Rs 9,826

Thus, the required amount is Rs 9,826.

**PAGE NO 14.15:**

**Question 14:**

**Find the compound interest on Rs 15625 for 9 months, at 16% per annum, compounded quarterly.**

**ANSWER:**

Given: P = Rs 15,625

R = 16% = 164 = 4% quarterly

n = 9 months = 3 quarters

We know that:A = P(1 + R/100)^{n }

= Rs 15,625(1 + 4/100)Â³

= Rs 15,625(1.04)Â³

= Rs 17,576

Also,CI = A âˆ’ P

= Rs 17,576 âˆ’ Rs 15,625

= Rs 1,951

Thus, the required compound interest is Rs 1,951.

**PAGE NO 14.15:**

**Question 15:**

**Rekha deposited Rs 16000 in a foreign bank which pays interest at the rate of 20% per annum compounded quarterly, find the interest received by Rekha after one year.**

**ANSWER:**

Given:P = Rs 16,000

R = 20% p.a.

n = 1 year

We know that:A = P(1 + R/100)^{n}

When compounded quarterly, we have:A = P(1 + R/400)^{4n}

= Rs 16,000(1 + 20/400)^{4 }

= Rs 16,000(1.05)^{4}

= Rs 19,448.10

Also,CI = A âˆ’ P

= Rs 19,448.1 âˆ’ Rs 16,000

= Rs 3,448.10

Thus, the interest received by Rekha after one year is Rs 3,448.10.

**PAGE NO 14.15:**

**Question 16:**

**Find the amount of Rs 12500 for 2 years compounded annually, the rate of interest being 15% for the first year and 16% for the second year.**

**ANSWER:**

Given: P = Rs 12,500

R_{1 } = 15% p.a.

R_{2} = 16% p.a.

âˆ´ Amount after two years = P(1 + R_{1}/100)(1 + R_{2}/100)

= Rs 12,500(1 + 15/100)(1 + 16/100)

= Rs 12,500(1.15)(1.16)

= Rs 16,675

Thus, the required amount is Rs 16,675.

**PAGE NO 14.15:**

**Question 17:**

**Ramu borrowed Rs 15625 from a finance company to buy a scooter. If the rate of interest be 16% per annum compounded annually, what payment will he have to make after ****years?**

**ANSWER:**

Given: P = Rs 15,625

R = 16% p.a.

n = years

âˆ´ Amount after years = P

= Rs 15,625

= Rs 15,625(1.16)Â²(1.04)

= Rs 21,866

Thus, the required amount is Rs 21,866.

**PAGE NO 14.15:**

**Question 18:**

**What will Rs 125000 amount to at the rate of 6%, if the interest is calculated after every 3 months?**

**ANSWER:**

Because interest is calculated after every 3 months, it is compounded quarterly.

Given:

P = Rs 125,000

R = 6% p.a. = 6/4% quarterly = 1.5% quarterly

n = 4

So,A = P(1 + R/100)^{n }

= 125,000(1 + 1.5/100)^{4}

= 125,000(1.015)^{4}

= 132,670 (approx)

Thus, the required amount is Rs 132,670.

**PAGE NO 14.15:**

**Question 19:**

**Find the compound interest at the rate of 5% for three years on that principal which in three years at the rate of 5% per annum gives Rs 12000 as simple interest.**

**ANSWER:**

According to the given values, we have:

= 80,000

The principal is to be compounded annually.

So, A = P(1 + R/100)^{n }

= 80,000(1 + 5/100)Â³

= 80,000(1.05)Â³

= 92,610

Now,CI = A âˆ’ P

= 92,610 âˆ’ 80,000

= 12,610

Thus, the required compound interest is Rs 12,610.

**PAGE NO 14.15:**

**Question 20:**

**A sum of money was lent for 2 years at 20% compounded annually. If the interest is payable half-yearly instead of yearly, then the interest is Rs 482 more. Find the sum.**

**ANSWER:**

A = P(1 + R/100)^{n}

Also, P = A âˆ’ CI

Let the sum of money be Rs x.

If the interest is compounded annually, then:

A_{1} = x(1 + 20/100)Â²

= 1.44x

âˆ´ CI = 1.44x âˆ’ x

= 0.44x ...(1)

If the interest is compounded half âˆ’ yearly, then:

A_{2 } = x(1 + 10/100)^{4 }

= 1.4641x

âˆ´ CI = 1.4641x âˆ’ x

= 0.4641x ...(2)

It is given that if interest is compounded half âˆ’ yearly, then it will be Rs 482 more.

âˆ´0.4641x = 0.44x + 482 [From (1) and (2)]

0.4641x âˆ’ 0.44x = 482

0.0241x = 482

x = 482/0.0241

= 20,000

Thus, the required sum is Rs 20,000.

**PAGE NO 14.15:**

**Question 21:**

**Simple interest on a sum of money for 2 years at 6.5% per annum is Rs 5200. What will be the compound interest on the sum at the same rate for the same period?**

**ANSWER:**

= 40,000

Now,

A = P(1 + R/100)^{n }

= 40,000(1 + 6.5/100)Â²

= 40,000(1.065)Â²

= 45,369

Also,CI = A âˆ’ P

= 45,369 âˆ’ 40,000

= 5,369

Thus, the required compound interest is Rs 5,369

**PAGE NO 14.15:**

**Question 22:**

**Find the compound interest at the rate of 5% per annum for 3 years on that principal which in 3 years at the rate of 5% per annum gives Rs 1200 as simple interest.**

**ANSWER:**

We know that:

= 8,000

Now,

A = P(1 + R/100)n

= 8,000(1 + 5/100)Â³

= 8,000(1.05)Â³ = 9,261

Now,CI = A âˆ’ P

= 9,261 âˆ’ 8,000

= 1,261

Thus, the required compound interest is Rs 1,261.