**Comparing Quantities**

**Question 1.****Calculate the amount and compound interest on(a)** ₹ 10,800 for 3 years at 12 % per annum compounded annually.

**(b)**₹ 18,000 for 2 years at 10% per annum compounded annually.

**(c)**₹ 62,500 for 1 years at 8% per annum compounded half yearly.

**(d)**₹ 8,000 for 1 year at 9% per annum compounded half yearly. (You could use the year by year calculation using SI formula to verify)

**(e)**₹ 10,000 for 1 year at 8% per annum compounded half yearly.

**Solution:**

**Question 2.****Kamala borrowed ₹ 26,400 from a Bank to buy a scooter at a rate of 15% p.a. compounded yearly. What amount will she pay at the end of 2 years and 4 months to clear the loan?**[

**Hint**: Find A for 2 years with interest is compounded yearly and then find SI on the 2nd year amount for years)

**Solution:**

Here, P = ₹ 26400, R =15% per annum

and n = 2 years 4 months =2 years.

Hence, Kamala will pay ₹ 36659.70 to the bank.

**Question 3.****Fabina borrows ? 12,500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest and by how much? .**

**Solution:**

In case of Fabina :

P = ₹ 12500, R =12% per annum and T =3 years. Then,

Hence, Fabina pays 362.50 more as interest ₹ (4500 – 4137.50), i.e., ₹ 362.50 more as interest.

**Question 4.****I borrowed ₹ 12,000 from Jamshed at 6% per annum simple interest for 2 years. Had I borrowed this sum at 6% per annum compound interest, what extra amount would I have to pay?**

**Solution:**

Here, P = ₹ 12000, R = 6% per annum and T = 2 years.

So, I have to pay ₹ (1483.20 -1440), i.e., ₹ 43.20 in excess.

**Question 5.****Vasudevan invested ₹ 60,000 at an interest rate of 12% per annum compounded half-yearly. What amount would he get(i)** after 6 months?

**(ii)**after 1 year.

**Solution:**

Here, Principal =₹ 60000, Rate = 12% per annum = 6%per half-year.**(i)** Time = 6 months = 1 half-year

**Question 6.****Arif took a loan of ? 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after 1 years if the interest is 2(i)** compounded annually

**(ii)**compounded half-yearly.

**Solution:**

Here, P = ₹ 80000

Rate = 10% per annum = 5% per half-year,

Time = 1 years = 3 half-years.

**Question 7.****Maria invested ? 8,000 in a business. She would he paid interest at 5% per annum compounded annually. Find(i)** The amount credited against her name at the end of the second year.

**(ii)**The interest for the 3rd year.

**Solution:**

**Question 8.****Find the amount and the compound interest on ? 10,000 for 1 years at 10% per annum, compounded half-yearly. Would this interest be more than the interest he would get if it was compounded annually?**

**Solution:**

Here, Principal = ? 10000

Time = 1 years = 3 half years,

This interest is more than the interest that he would get if it was compounded annually.

**Question 9.****Find the amount which Ram will get on ₹ 4096, if he gave it for 18 months at 12 % per annum, interest being compounded half yearly.**

**Solution:**

Here, Principal = ₹ 4096,

Time = 18 months = 3 half years

**Question 10.****The population of a place increased to 54,000 in 2003 at a rate of 5% per annum(i)** find the population in 2001.

**(ii)**what would be its population in 2005?

**Solution:**

**Question 11.****In a Laboratory, the count of bacteria in a certain experiment was increasing at the rate of 2.5% per hour. Find the bacteria at the end of 2 hours if the count was initially 5,06,000.**

**Solution:**

We have, P = Original count of bacteria = 506000;

Rate of increase = R = 2.5% per hour, Time = 2 hours.

**Question 12.****A scooter was bought at ? 42,000. Its value depreciated at the rate of 8% per annum. Find its value after one year.**

**Solution:**

We have, V_{0} = Initial value = ₹ 42000

R = Rate of depreciation = 8% p.a.