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**Unit 6 Brain Teaser | Compound Interest | DAV Solution Class 8 Secondary Mathematics**

**Q1A. Tick the correct option. **

**(i) For a given rate of interest and time, what is more profitable to the depositor? **

**(a) compound interest (b) simple interest (c) both are equally profitable (d) cannot be determined **

**(ii) A sum of Rs. 10,000 at 8% per annum for six months compounded quarterly amounts to **

**(a) 400 (b) 404 (c) 408 (d) 10,404 **

**(iii) In A = p(1 + R/100)^n , A stands for **

**(a) time period (b) principal (c) principal+interest (d) interest**

**(iv) If the number of conversion periods is greater than or equal to 2, then compound interest is**

**(a) less than simple interest.**

**(b) greater than simple interest.**

**(c) less than or equal to simple interest.**

**(v) Reema wants to do a one-year deposit. She should opt for**

**(a) a simple interest of 10%.**

**(b) a compound interest of 10% compounded quarterly.**

**(c) a compound interest of 10% compounded annually.**

**(d) a compound interest of 10% compounded half-yearly.**

**Q1B. Answer the following questions. **

**(i) Find the compound interest on Rs. 1,000 at 10% per annum for two years. **

**(ii) If Rs. 6,000 is deposited for two years at 4% per annum compounded quarterly. then find the time period and rate to compute compound interest. **

**(iii) The value of a machine worth Rs. 5,00,000 depreciates at the rate of 10% every year. In how many years will its value be Rs. 3,64,500? **

**(iv) Find the difference between the compound interest and simple interest on Rs. 5000 for two years at 5% per annum. **

**(v) If Rs. 20,000 is deposited for three years at 5% compounded annually, then what will be the principal for the second year?**

**2. Preeti invested ₹ 50,000 at 8% per annum for 3 years and the interest is compounded annually. Calculate: **

**(i) The amount standing to her credit at the end of the second year. **

**(ii) The interest for the third year. **

**3. A man had ₹75,000. He invested ₹35,000 in a company which pays him 9% interest per annum and he invested rest of the money in another company which pays him 9.5% interest per annum. Find the total compound interest received by him after 2 years. **

**4. A certain sum of money at compound interest becomes ₹7,396 in 2 years and ₹7,950.70 in 3 years. Find the rate of interest. **

**5. Pooja started a business by investing ₹2,00,000. During the first three successive years, she earned a profit of 5%, 8% and 12% per annum respectively. If in each year, the profit was added on the capital at the end of the previous year, calculate her total profit after 3 years. **

**6. Mahesh borrowed a certain sum for 2 years at simple interest from Bhim. Mahesh lent this sum to Vishnu at the same rate for 2 years compound interest. At the end of 2 years, Mahesh received 410 as compound interest but paid ₹400 as simple interest. Find the sum and rate of interest. **

**7. A man invested ₹ 1,000 is invested for three years at 11% simple interest per annum and another 1,000 is invested at 10% compound interest per annum compounded annually for 3 years. Find which investment is better.**

**8. M/s Heera Associates let out ₹4,00,000 for 1 year at 16% p.a. compounded annually. How much they could earn if the interest is compounded (i) half-yearly (ii) quarterly? **

**9. Sirish borrowed a sum of ₹1,63,840 at 12.5% p.a. compounded annually. On the same day, he lent out the same amount to Sahej at the same rate of interest but compounded half-yearly. Find his gain after 2 years.**

**10. The annual rate of growth in population of a certain city is 8%. If its present population is ₹1,96,830, what was the population 3 years ago?**

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