### Chapter 14 Compound Interest – Exercise 14.2 | Set 1

**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?**

**Solution:**

We have,

Principal (p) = Rs 10000

Rate (r) = 20% per annum

Time (t) = 2years

By using the formula,

A = P (1 + R/100)

^{n}= 10000 (1 + 20/100)

^{2}= 10000 (120/100)

^{2 }= Rs 14400

When the interest is compounded half-yearly,New values are

Rate of interest becomes= 20/2% = 10%

Time = 2×2 years = 4years

By using the formula,

A = P (1 + R/100)

^{n}Substituting the values we have,

= 10000 (1 + 10/100)

^{4}= 10000 (110/100)

^{4 }= Rs 14641∴ Rakesh could earn Rs (14641 – 14400) = Rs 241 more

**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.**

**Solution:**

Given:

Principal (p) = Rs 245760

Rate (r) = 12.5% per annum

Time (t) = 2years

By using the formula,

A = P (1 + R/100)

^{n}Substituting the values we have,

= 245760 (1 + 12.5/100)

^{2}= 245760 (112.5/100)

^{2}= Rs 311040

Now, When compounded semi-annually,Rate = 12.5/2% = 6.25%

Time = 2×2 years = 4years

By using the formula,

A = P (1 + R/100)

^{n}Substituting the values we have,

= 245760 (1 + 6.25/100)

^{4}= 245760 (106.25/100)

^{4 }= Rs 313203.75∴ Romesh gain is Rs (313203.75 – 311040) = Rs 2163.75

**Question 13. Find the amount that David would receive if he invests Rs. 8192 for 18 months at 12 ½ % per annum, the interest being compounded half-yearly.**

**Solution:**

Given,

Principal (p) = Rs 8192

Rate (r) = 12 ½ % per annum = 25/2×2 = 25/4% = 12.5/2% (half-yearly)

Time (t) = 18 months = 18/12 = 1 ½ years = (3/2) × 2 = 3years

By using the formula,

A = P (1 + R/100)

^{n}Substituting the values we have,

= 8192 (1 + 12.5/2×100)

^{3}= 8192 (212.5/200)

^{3}= Rs 9826

∴ Amount is Rs 9826

**Question 14. Find the compound interest on Rs. 15625 for 9 months, at 16% per annum, compounded quarterly.**

**Solution:**

Given,

Principal (p) = Rs 15625

Rate (r) = 16% per annum = 16/4 = 4% (quarterly)

Time (t) = 9 months = 9/12 × 4 = 3quarters of a year

By using the formula,

A = P (1 + R/100)

^{n}Substituting the values we have,

= 15625 (1 + 4/100)

^{3}= 15625 (104/100)

^{3}= Rs 17576

∴ CI = Rs 17576 – 15625 = Rs 1951

**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**

**Solution:**

Given is,

Principal (p) = Rs 16000

Rate (r) = 20% per annum = 20/4 = 5% (quarterly)

Time (t) = 1 year = 4 quarters of a year

By using the formula,

A = P (1 + R/100)

^{n}Substituting the values we have,

= 16000 (1 + 5/100)

^{4}= 16000 (105/100)

^{4}= Rs 19448.1∴ CI = Rs 19448.1 – 16000 = Rs 3448.1

**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.**

**Solution:**

We have the following set of values,

Principal (p) = Rs 12500

Rate1 (r) = 15% and Rate2 = 16%

Time (t) = 2 years

By using the formula,

A = P (1 + R1/100 × 1 + R2/100) = 12500

Substituting the values we have,

(1 + 15/100 × 1 + 16/100) = 12500 (1.15 × 1.16)

= Rs 16675

∴ Amount after two years is Rs 16675

**Question 17. Ramu borrowed Rs. 15625 from a finance company to buy scooter. If the rate of interest be 16% per annum compounded annually, what payment will he have to make after 2 ¼ years?**

**Solution:**

Given details are,

Principal (p) = Rs 15625

Rate (r) = 16%

Time (t) = 2 ¼ years

By using the formula,

A = P (1 + R/100 × 1 + R/100)= 15625

Substituting the values we have,

(1 + 16/100)

^{2}× (1 + (16/4)/100)= 15625(1 + 16/100)

^{2}× (1 + 4/100)= 15625(1.16)

^{2}× (1.04)= Rs 21866∴ Amount after 2 ¼ years is Rs 21866

**Question 18. What will Rs. 125000 amount to at the rate of 6%, if the interest is calculated after every four months?**

**Solution:**

Given,

Principal (p) = Rs 125000

Rate (r) = 6% per annum

Time (t) = 1 year

Since interest is compounded after 4months, interest will be counted as 6/3 = 2% and,

Time will be 12/4 = 3quarters

By using the formula,

A = P (1 + R/100)

^{n}Substituting the values we have,

= 125000 (1 + 2/100)

^{3}= 125000 (102/100)

^{3}= Rs 132651

∴ Amount is Rs 132651

**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.**

**Solution:**

Given,

Simple interest (SI) = Rs 12000

Rate (r) = 5% per annum

Time (t) = 3 years

SI = (PTR)/100P

= (SI×100)/(T×R)

Solving the equations,

= (12000×100) / (3×5)

= 1200000/15= 80000

By using the formula,

A = P (1 + R/100)

^{n}Substituting the values we have,

= 80000 (1 + 5/100)

^{3}= 80000 (105/100)

^{3}= Rs 92610

∴ CI = Rs 92610 – 80000 = Rs 12610

**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.**

**Solution:**

We have,

Rate (r) = 20% per annum = 20/2 = 10% (half yearly)

Time (t) = 2 years = 2 × 2 = 4 half years

Principal be = Rs P

P (1 + R/100)

^{n}– P (1 + R/100)^{n}= 482P (1 + 10/100)

^{4}– P (1 + 20/100)^{2}= 482P (110/100)

^{4}– P (120/100)^{2}= 482P (1.4641) – P (1.44)

= 4820.0241P

= 482P = 482/0.0241

= 20000

∴ Amount is Rs 20000

**Question 21. Simple interest on a sum of money for 2 years at 6 ½ % per annum is Rs. 5200. What will be the compound interest on the sum at the same rate for the same period?**

**Solution:**

Given is,

Rate = 6 ½ % per annum = 13/2%

Simple Interest (SI) = Rs 5200

Time (t) = 2 years

By using the formula,

SI = (PTR)/100P = (SI×100) / (T×R)

= (5200×100) / (2×13/2)

= (5200×100×2) / (2×13)

= 1040000/26

= Rs 40000

Now, P = Rs 40000R

= 13/2% = 6.5%T = 2years

By using the formula,

A = P (1 + R/100)

^{n}Substituting the values we have,

= 40000 (1 + 6.5/100)

^{2}= 40000 (106.5/100)

^{2}= Rs 45369

∴ CI = Rs 45369 – 40000 = Rs 5369

**Question 22. What will be 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.**

**Solution:**

Rate = 5 % per annum

Simple Interest (SI) = Rs 1200

Time (t) = 3 years

By using the formula,

SI = (PTR)/100P = (SI×100) / (T×R)

= (1200×100) / (3×5)

= 120000/15

= Rs 8000

Now, P = Rs 8000R

= 5%T = 3years

By using the formula,

A = P (1 + R/100)

^{n}= 8000 (1 + 5/100)

^{3}= 8000 (105/100)

^{3}= Rs 9261

∴ CI = Rs 9261 – 8000 = Rs 1261