# Simple and Compound Interest Aptitude Questions and Answers:

#### Overview:

 Questions and Answers Type: MCQ (Multiple Choice Questions). Main Topic: Quantitative Aptitude. Quantitative Aptitude Sub-topic: Simple and Compound Interest Aptitude Questions and Answers. Number of Questions: 10 Questions with Solutions.

1. A man lent $$Rs.100$$ at compound interest of $$10 \ \%$$ per annum for first year and $$20 \ \%$$ per annum for second year compounded annually. Find the total amount after two years?

1. $$Rs.130$$
2. $$Rs.132$$
3. $$Rs.135$$
4. $$Rs.138$$

Answer: (b) $$Rs.132$$

Solution: Given, principal amount (P) = $$Rs.100$$

rate of interest for first year $$(R_1)$$ = $$10 \ \%$$

rate of interest for second year $$(R_2)$$ = $$20 \ \%$$

then total amount after two years, $$A = P \ \left(1 + \frac{R_1}{100}\right) \ \left(1 + \frac{R_2}{100}\right)$$ $$A = 100 \ \left(1 + \frac{10}{100}\right) \ \left(1 + \frac{20}{100}\right)$$ $$= 100 \times \frac{11}{10} \times \frac{6}{5}$$ $$A = Rs.132$$

1. Rahul deposited $$Rs.500$$ in a bank at the compound interest of $$20 \ \%$$ per annum for first year compounded annually and $$50 \ \%$$ per annum for second year compounded half-yearly. Find the total amount after two years Rahul will get from the bank?

1. $$Rs.937.5$$
2. $$Rs.942.3$$
3. $$Rs.946.8$$
4. $$Rs.936.6$$

Answer: (a) $$Rs.937.5$$

Solution: Given, principal amount (P) = $$Rs.500$$

rate of interest for first year $$(R_1)$$ = $$20 \ \%$$

rate of interest for second year $$(R_2)$$ = $$50 \ \%$$

then total amount after two years, $$A = P \ \left(1 + \frac{R_1}{100}\right) \ \left(1 + \frac{R_2/2}{100}\right)^2$$ $$A = 500 \ \left(1 + \frac{20}{100}\right) \ \left(1 + \frac{25}{100}\right)^2$$ $$= 500 \times \frac{6}{5} \times \frac{5}{4} \times \frac{5}{4}$$ $$A = Rs.937.5$$

1. A girl deposited $$Rs.1000$$ in a bank at the compound interest of $$10 \ \%$$ per annum for first year compounded half-yearly and $$40 \ \%$$ per annum for second year compounded quarterly. Find the total amount after two years the girl will get from the bank?

1. $$Rs.1524.37$$
2. $$Rs.1614.17$$
3. $$Rs.1725.12$$
4. $$Rs.1847.57$$

Answer: (b) $$Rs.1614.17$$

Solution: Given, principal amount (P) = $$Rs.1000$$

rate of interest for first year $$(R_1)$$ = $$10 \ \%$$

rate of interest for second year $$(R_2)$$ = $$40 \ \%$$

then total amount after two years, $$A = P \ \left(1 + \frac{R_1/2}{100}\right)^2 \ \left(1 + \frac{R_2/4}{100}\right)^4$$ $$A = 1000 \ \left(1 + \frac{5}{100}\right)^2 \ \left(1 + \frac{10}{100}\right)^4$$ $$= 1000 \times \left(\frac{21}{20}\right)^2 \times \left(\frac{11}{10}\right)^4$$ $$= 1000 \times \frac{441}{400} \times \frac{14641}{10000}$$ $$A = Rs.1614.17$$

1. A man lent $$Rs.700$$ from the bank at the compound interest of $$40 \ \%$$ per annum compounded half-yearly. Find the amount, the man will have to pay after two years?

1. $$Rs.1226.15$$
2. $$Rs.1258.46$$
3. $$Rs.1451.52$$
4. $$Rs.1652.89$$

Answer: (c) $$Rs.1451.52$$

Solution: Given, principal amount (P) = $$Rs.700$$

rate of interest (R) = $$40 \ \%$$

time period (n) = $$2$$ years

then total amount after two years, $$A = P \ \left(1 + \frac{R/2}{100}\right)^{2n}$$ $$A = 700 \ \left(1 + \frac{20}{100}\right)^4$$ $$A = 700 \ \left(\frac{6}{5}\right)^4$$ $$A = Rs.1451.52$$

1. If the interest compounded at the rate of $$10 \ \%$$ per annum for three years is $$Rs.1000$$. Find the principal amount?

1. $$Rs.3021.14$$
2. $$Rs.3124.61$$
3. $$Rs.3358.33$$
4. $$Rs.3568.14$$

Answer: (a) $$Rs.3021.14$$

Solution: Given, compound interest (CI) = $$Rs.1000$$

rate of interest (R) = $$10 \ \%$$

time period (n) = $$3$$ years,$$CI = P \ \left(1 + \frac{R}{100}\right)^n - P$$ $$1000 = P \ \left(1 + \frac{10}{100}\right)^3 - P$$ $$1000 = P \ \left[\left(\frac{11}{10}\right)^3 - 1\right]$$ $$1000 = P \ \left[\left(\frac{1331}{1000}\right) - 1\right]$$ $$P = Rs.3021.14$$

1. Sachin deposited $$Rs.100$$ at the compound interest of $$5 \ \%$$ per annum compounded yearly for first year, $$10 \ \%$$ per annum compounded yearly for second year and $$20 \ \%$$ per annum compounded half-yearly for third year. Find the total amount after three years?

1. $$Rs.142.3$$
2. $$Rs.141.5$$
3. $$Rs.140.6$$
4. $$Rs.139.7$$

Answer: (d) $$Rs.139.7$$

Solution: Given, principal amount (P) = $$Rs.100$$

rate of interest for first year $$(R_1)$$ = $$5 \ \%$$

rate of interest for second year $$(R_2)$$ = $$10 \ \%$$

rate of interest for third year $$(R_3)$$ = $$20 \ \%$$

then total amount after three years,

$$A = P \left(1 + \frac{R_1}{100}\right) \left(1 + \frac{R_2}{100}\right) \left(1 + \frac{R_3/2}{100}\right)^2$$

$$A = P \left(1 + \frac{R_1}{100}\right) \left(1 + \frac{R_2}{100}\right) \\ \left(1 + \frac{R_3/2}{100}\right)^2$$

$$A = 100 \left(1 + \frac{5}{100}\right) \left(1 + \frac{10}{100}\right) \left(1 + \frac{10}{100}\right)^2$$

$$A = 100 \left(1 + \frac{5}{100}\right) \left(1 + \frac{10}{100}\right) \\ \left(1 + \frac{10}{100}\right)^2$$

$$= 100 \times \left(\frac{21}{20}\right) \times \left(\frac{11}{10}\right)^3$$ $$A = Rs.139.7$$

1. Calculate the simple interest on the principal amount $$Rs.8000$$ at the rate of interest $$6 \ \%$$ per annum for three years?

1. $$Rs.1360$$
2. $$Rs.1400$$
3. $$Rs.1418$$
4. $$Rs.1440$$

Answer: (d) $$Rs.1440$$

Solution: Given, principal amount (P) = $$Rs.8000$$

rate of interest (R) = $$6 \ \%$$

time period (T) = $$3$$ years, then $$SI = \frac{P \ R \ T}{100}$$ $$= \frac{8000 \times 6 \times 3}{100}$$ $$SI = Rs.1440$$

1. In how many years a principal amount become three times if the rate of interest is $$4 \ \%$$ per annum?

1. $$40 \ years$$
2. $$45 \ years$$
3. $$50 \ years$$
4. $$55 \ years$$

Answer: (c) $$50 \ years$$

Solution: Given, Let principal amount (P) = $$Rs.k$$

simple interest (SI) = $$3k - k$$ = $$Rs.2k$$

rate of interest (R) = $$4 \ \%$$

Hence, $$SI = \frac{P \ R \ T}{100}$$ $$2k = \frac{k \times 4 \times T}{100}$$ $$T = 50 \ years$$

1. Vikash deposited $$Rs.1200$$ in a bank at the rate of $$20 \ \%$$ per annum compounded quarterly. Find the total amount after one year?

1. $$Rs.1458.6$$
2. $$Rs.1486.1$$
3. $$Rs.1488.6$$
4. $$Rs.1492.8$$

Answer: (a) $$Rs.1458.6$$

Solution: Given, principal amount (P) = $$Rs.1200$$

rate of interest (R) = $$20 \ \%$$

time period (n) = $$1$$ years

then total amount after one year, $$A = P \ \left(1 + \frac{R/4}{100}\right)^{4n}$$ $$A = 1200 \ \left(1 + \frac{5}{100}\right)^4$$ $$A = 1200 \ \left(\frac{21}{20}\right)^4$$ $$A = Rs.1458.6$$

1. A women lent $$Rs.2200$$ from the bank at the compound interest of $$10 \ \%$$ per annum for first year compounded annually and $$20 \ \%$$ per annum for second year compounded half-yearly. Find the total amount after two years?

1. $$Rs.2834.6$$
2. $$Rs.2874.4$$
3. $$Rs.2928.2$$
4. $$Rs.2936.3$$

Answer: (c) $$Rs.2928.2$$

Solution: Given, principal amount (P) = $$Rs.2200$$

rate of interest for first year $$(R_1)$$ = $$10 \ \%$$

rate of interest for second year $$(R_2)$$ = $$20 \ \%$$

then total amount after two years, $$A = P \ \left(1 + \frac{R_1}{100}\right) \ \left(1 + \frac{R_2/2}{100}\right)^2$$ $$A = 2200 \ \left(1 + \frac{10}{100}\right) \ \left(1 + \frac{10}{100}\right)^2$$ $$= 2200 \times \frac{11}{10} \times \frac{11}{10} \times \frac{11}{10}$$ $$A = Rs.2928.2$$