Comparing Quantities

Exercise 8.3

Part 1

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`

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)xx(23)/(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`