## Compound Interest Questions and Answers Part-8

1. A man borrow Rs. 4000 at 15%, compound rate of interest. At the end of each year he pays back Rs. 1500. How much amount should be pay at the end of the third year to clear all his dues ?
a) Rs. 874.75
b) Rs. 824.50
c) Rs. 924.25
d) Rs. 974.25

Explanation:
\eqalign{ & {\text{Amount after }}{{\text{1}}^{{\text{st}}}}{\text{ year}} \cr & {\text{ = Rs}}{\text{. }}\left[ {4000\left( {1 + \frac{{15}}{{100}}} \right) - 1500} \right] \cr & = {\text{Rs}}{\text{. }}\left[ {\left( {4000 \times \frac{{23}}{{20}}} \right) - 1500} \right] \cr & = {\text{Rs}}{\text{. }}\left( {4600 - 1500} \right) \cr & = {\text{Rs}}{\text{. }}3100 \cr & {\text{Amount after }}{{\text{2}}^{{\text{nd}}}}{\text{ year}} \cr & {\text{ = Rs}}{\text{. }}\left[ {3100\left( {1 + \frac{{15}}{{100}}} \right) - 1500} \right] \cr & = {\text{Rs}}{\text{. }}\left[ {\left( {3100 \times \frac{{23}}{{20}}} \right) - 1500} \right] \cr & = {\text{Rs}}{\text{. }}\left( {3565 - 1500} \right) \cr & = {\text{Rs}}{\text{. }}2065 \cr & {\text{Amount after }}{{\text{3}}^{{\text{rd}}}}{\text{ year}} \cr & {\text{ = Rs}}{\text{. }}\left[ {2065\left( {1 + \frac{{15}}{{100}}} \right) - 1500} \right] \cr & = {\text{Rs}}{\text{. }}\left[ {\left( {2065 \times \frac{{23}}{{20}}} \right) - 1500} \right] \cr & = {\text{Rs}}{\text{. }}\left( {2374.75 - 1500} \right) \cr & = {\text{Rs}}{\text{. }}874.75 \cr}

2. A certain sum of amounts to Rs. 5832 in 2 years at 8% per annum compound interest, the sum is = ?
a) Rs. 5000
b) Rs. 5200
c) Rs. 5280
d) Rs. 5400

Explanation: $${\text{Rate 8% = }}\frac{2}{{25}}$$
 Principal Amount 25 27 25 27 625 729 ↓ × 8 ↓ × 8 5000 5832
Required sum = Rs. 5000

3. A person deposited a sum of of Rs 6000 in a bank at 5% per annum simple interest. Another person deposited Rs 5000 at 8% per annum compound interest. After two years, the difference of their interest will be =
a) Rs. 230
b) Rs. 232
c) Rs. 832
d) Rs. 600

Explanation:
\eqalign{ & {\text{Principal (}}{{\text{P}}_1}{\text{) = Rs. 6000}} \cr & {\text{Time (t) = 2 years}} \cr & {\text{Rate % = 5% }} \cr & {\text{Simple interest}} {\text{ = }}\frac{{6000 \times 5 \times 2}}{{100}}{\text{ = Rs. 600}} \cr & {\text{Principal (}}{{\text{P}}_2}{\text{) = Rs. 5000}} \cr & {\text{Time (t) = 2 years}} \cr & {\text{Rate % = 8% }} \cr}
2 year effective rate for Compound interest
\eqalign{ & = 8 + 8 + \frac{{8 \times 8}}{{100}} = 16.64\% \cr & {\text{Compound}}\,{\text{Interest}} \cr & {\text{ = 5000}} \times \frac{{16.64}}{{100}} = {\text{Rs}}{\text{. 832}} \cr & {\text{Difference}} {\text{ = Rs}}{\text{. }}\left( {832 - 600} \right) \cr & = {\text{Rs}}{\text{.}}\,232 \cr & {\text{ }} \cr}

4. A man invests Rs. 5000 for 3 years at 5% p.a. compound interest reckoned yearly. Income tax at the rate of 20% on the interest earned is deducted at the end of each year. Find the amount at the end of the third year = ?
a) Rs. 5624.32
b) Rs. 5627.20
c) Rs. 5630.50
d) Rs. 5788.125

Explanation:
\eqalign{ & {\text{C}}{\text{.I}}{\text{. earned during }}{{\text{1}}^{{\text{st}}}}{\text{ year}} \cr & {\text{= }}\,{\text{Rs}}{\text{.}}\left[ {5000\left( {1 + \frac{5}{{100}}} \right) - 5000} \right]{\text{ }} \cr & = {\text{Rs}}{\text{. }}\left( {5250 - 5000} \right) \cr & = {\text{Rs}}{\text{. 250}} \cr & {\text{Amount after }}{{\text{1}}^{{\text{st}}}}{\text{ year}} \cr & = {\text{Rs}}{\text{. }}\left( {5250 - 20\% {\text{ of }}250} \right) \cr & = {\text{Rs}}{\text{.}}\left( {5250 - 50} \right){\text{ }} \cr & {\text{= }}\,{\text{Rs}}{\text{.}}\,{\text{5200 }} \cr & {\text{C}}{\text{.I}}{\text{. earned during }}{{\text{2}}^{{\text{nd}}}}{\text{ year}} \cr & = {\text{Rs}}{\text{.}}\left[ {5200\left( {1 + \frac{5}{{100}}} \right) - 5200} \right]{\text{ }} \cr & = {\text{Rs}}{\text{. }}\left( {5460 - 5200} \right) \cr & = {\text{Rs}}{\text{.260 }} \cr & {\text{Amount after }}{{\text{2}}^{{\text{nd}}}}{\text{ year}} \cr & {\text{= Rs}}{\text{. }}\left( {5460 - 20\% {\text{ of }}260} \right) \cr & {\text{= Rs}}{\text{. }}\left( {5460 - 52} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{5408 }} \cr & {\text{C}}{\text{.I}}{\text{. earned during }}{{\text{3}}^{{\text{rd}}}}{\text{ year}} \cr & {\text{= Rs}}{\text{. }}\left[ {5408\left( {1 + \frac{5}{{100}}} \right) - 5408} \right] \cr & = {\text{Rs}}{\text{. }}\left( {5678.40 - 5408} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{270}}{\text{.40 }} \cr & {\text{Amount after }}{{\text{3}}^{{\text{rd}}}}{\text{ year}} \cr & = {\text{Rs}}{\text{. }}\left( {5678.40 - 20\% \,{\text{of }}270.40} \right) \cr & = {\text{Rs}}{\text{. }}\left( {5678.40 - 54.08} \right) \cr & = {\text{Rs}}{\text{. 5624}}{\text{.32}} \cr}

5. At a certain rate per annum, the simple interest on a sum of money for one year is Rs. 260 and the compound interest on the same sum for two years is Rs. 540.80. The rate of interest per annum is =
a) 4%
b) 6%
c) 8%
d) 10%

Explanation:
\eqalign{ & {\text{SI for 1 year}} {\text{ = Rs 260}} \cr & {\text{SI for 2 year}} {\text{ = 260}} \times {\text{2}} \cr & {\text{ = Rs}}{\text{. 520 }} \cr & {\text{Difference in (CI}} - {\text{SI)}} \cr & \left( {540.80 - 520} \right){\text{ = Rs 20}}{\text{.8}} \cr & {\text{Required rate % }} \cr & {\text{ = }}\frac{{20.8}}{{260}} \times {\text{100}} \cr & {\text{ = 8% }} \cr}

6. In how many years will a sum of Rs. 800 at 10% per annum compounded semi annually become Rs. 926.10?
a) $$1\frac{1}{3}$$ years
b) $$1\frac{1}{2}$$ years
c) $$2\frac{1}{3}$$ years
d) $$2\frac{1}{2}$$ years

Explanation:
\eqalign{ & {\text{Let the time be }}n{\text{ year}} \cr & {\text{800}} \times {\left( {1 + \frac{5}{{100}}} \right)^{2n}} = 926.10 \cr & {\left( {1 + \frac{5}{{100}}} \right)^{2n}} = \frac{{9261}}{{8000}} \cr & {\left( {\frac{{21}}{{20}}} \right)^{2n}} = {\left( {\frac{{21}}{{20}}} \right)^3} \cr & 2n = 3 \cr & n = \frac{3}{2} \cr & n = 1\frac{1}{2}{\text{years}} \cr}

7. A loan of Rs. 12300 at 5% per annum compound interest, is to be repaid in two equal annual installments at the end of every year. Find the amount of each installment ?
a) Rs. 6651
b) Rs. 6615
c) Rs. 6516
d) Rs. 6156

Explanation: $$5\% = \frac{1}{{20}} = \frac{{21 \to {\text{ Installment}}}}{{20 \to {\text{ Principal}}}}$$
 Year Principal Installment ⇒ I 20×21 → 21×21 ......(i) ⇒ II 400→ 441 .....(ii)
Since, installment is equal, hence multiply equation (i) by 21
Total principal = 420 + 400 = 820
820 units = Rs. 12300
1 units = Rs. 15
441 units = Rs. 6615
Each installment = Rs. 6615

8. An amount of Rs 6000 lent at 5% per annum compounded interest for 2 years will become =
a) Rs. 600
b) Rs. 6600
c) Rs. 6610
d) Rs. 6615

Explanation:
\eqalign{ & {\text{Amount = 6000}}{\left( {1 + \frac{5}{{100}}} \right)^2} \cr & {\text{Amount = 6000}} \times \frac{{21}}{{20}} \times \frac{{21}}{{20}} \cr & {\text{Amount = Rs. 6615}} \cr}

9. The simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is ?
a) Rs. 1550
b) Rs. 1650
c) Rs. 1750
d) Rs. 2000

\eqalign{ & {\text{C}}{\text{.I}}{\text{.}} {\text{ = Rs}}{\text{.}}\left[ {4000 \times {{\left( {1 + \frac{{10}}{{100}}} \right)}^2} - 4000} \right] \cr & = {\text{ Rs}}{\text{.}}\left( {4000 \times \frac{{11}}{{10}} \times \frac{{11}}{{10}} - 4000} \right) \cr & = {\text{Rs}}{\text{. 840}} \cr & {\text{Sum = Rs}}{\text{.}}\left( {\frac{{420 \times 100}}{{3 \times 8}}} \right) \cr & = {\text{Rs}}{\text{. }}1750 \cr}
\eqalign{ & {\text{Let P}} = {\text{Rs}}.100 \cr & {\text{S}}{\text{.I}}{\text{. = Rs}}.60{\text{ and}} \cr & {\text{T = 6 years}} \cr & {\text{R = }}\frac{{100 \times 60}}{{100 \times 6}}{\text{ = 10% p}}{\text{.a}}{\text{.}} \cr & {\text{P = Rs 12000,}} \cr & {\text{T = 3 years and}} \cr & {\text{R = 10% p}}{\text{.a}}{\text{.}} \cr & {\text{C}}{\text{.I}}{\text{. = Rs}}{\text{.}}\left[ {12000 \times \left\{ {{{\left( {1 + \frac{{10}}{{100}}} \right)}^3} - 1} \right\}} \right] \cr & = {\text{Rs}}{\text{.}}\left( {12000 \times \frac{{331}}{{1000}}} \right) \cr & = {\text{Rs}}{\text{. }}3972 \cr}