# Comparing Quantities

## Exercise 8.3

Question 1: Calculate the amount and compound interest on

(a) Rs 10,800 for 3 years at 12.5% per annum compounded annually.

Answer: A = P(1+(R)/(100))^t

P = 10800, R =12(1)/(2)% and t = 3 years

So, A = 10800(1+(25)/(200))^3

=10800(1+1/8)^3

=10800(9/8)^3

=10800xx9/8xx9/8xx9/8=15377.34

So, Interest = A –P

=15377.54-10800=4577.34

(b) Rs 18,000 for 2.5 years at 10% per annum compounded annually.

Answer: Amount =18000(1+(10)/(100))^2

=18000xx(11)/(10)xx(11)/(10)=21780

Interest after 2 years =21780-18000=3780

Interest after half year =21780xx(10)/(100)xx1/2=1089

Total interest after 2.5 years =3780+1089=4869

(c) Rs 62,500 for 1.5 years at 8% per annum compounded half yearly.

Answer: Amount after 1.5 year =62500(1+(4)/(100))^3

Rate has been halved because interest is compounded half yearly, time has been doubled for the same reason.

=62500xx(26)/(25)xx(26)/(25)xx(26)/(25)=70304

So, interest =70304-62500=7804

(d) Rs 8,000 for 1 year at 9% per annum compounded half yearly.

Answer: A=8000(1+(9)/(200))^2

=8000xx(209)/(200)xx(209)/(200)=8736.20

So, interest =8736.20-8000=736.20

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

Answer: A=10000(1+(4)/(100))^2

=10000xx(26)/(25)xx(26)/(25)=10816

So, interest =10816-10000=816

Alternate method: Calculating big multiplication can be tedious. Compound interest can also be calculated by finding yearly amount for each year separately.
1st half year 10000+400=10400
2nd half year 10400+416=10816

Question 2: Kamala borrowed Rs 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?

Solution: Amount after 1st year 26400 + 3960 = 30360
Amount after 2nd year 30360 + 4554 = 34914
To make things easier interest can be bifurcated into two parts of 10% and 5% as follows:
1st year 26400 + 2640 + 1320 = 30360
2nd year 30360 + 3036 + 1518 = 34914

A=26400(1+(15)/(100))^2

=26400xx(23)/(20)xx23)/(20)=34914

Question 3: Fabina borrows Rs 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?

Answer: Interest for Fabina =(P\xx\t\xx\r)/(100)

=(12500xx3xx12)/(100)=4500

Amount for Radha =12500(1+(10)/(100))^3

=12500xx(11)/(10)xx(11)/(10)xx(11)/(10)=16637.50

Interest for Radha = 16637.50-12500=4137.50
Interest paid by Fabina is Rs. 362.50 more than that paid by radha

Question 4: I borrowed Rs 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: The extra amount payable would be interest on the first year’s interest
1st year’s interest = 12000 xx 6%=720
Interest on 720 = 720 xx 6%=43.20
Extra amount payable = Rs. 43.20

Question 5: Vasudevan invested Rs 60,000 at an interest rate of 12% per annum compounded half yearly. What amount would he get

(i) after 6 months?

Solution: Amount = 60000+60000 xx 6%=60000+3600=63600

(ii) after 1 year?

Solution: Amount = 63600+63600 xx6% = 63600+3816=67416