## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 8 Simple and Compound Interest Objective Type Questions

**Mental Maths**

Question 1.

Fill in the blanks:

(i) The money borrowed (lent or invested) is called …………

(ii) the additional money paid by the borrower to the moneylender in lieu of the money used is called …………

(iii) In simple interest, the principal ………… for the whole loan period.

(iv) In compound interest the ………… goes on changing every conversion period.

(v) The time after which the interest is added each time to form a new principal is called …………

(vi) If the interest is compounded semi-annually then semi-annually rate is ………… of annual rate.

Solution:

(i) The money borrowed (lent or invested) is called principal.

(ii) the additional money paid by the borrower to the moneylender

in lieu of the money used is called interest.

(iii) In simple interest, the principal remains constant for the whole loan period.

(iv) In compound interest the principal goes on changing every conversion period.

(v) The time after which the interest is added each time to form

a new principal is called conversion period.

(vi) If the interest is compounded semi-annually

then semi-annually rate is half of annual rate.

Question 2.

State whether the following statements are true (T) or false (F):

(i) The interest paid by the banks, post offices, insurance companies is simple interest.

(ii) Compound interest is calculated on the amount of the previous year.

(iii) In compound interest, the principal remains constant for the whole period.

(iv) The time from one specified interest period to the next period is called conversion period.

(v) If the interest is compounded quarterly then there are 2 conversion periods in a year.

Solution:

(i) The interest paid by the banks, post offices,

insurance companies is simple interest. False

Correct:

It is compound interest.

(ii) Compound interest is calculated on

the amount of the previous year. True

(iii) In compound interest, the principal remains constant

for the whole period. False

Correct:

It goes on changing every conversion period,

(iv) The time from one specified interest period to the

next period is called conversion period.

True

(v) If the interest is compounded quarterly

then there are 2 conversion periods in a year.

False

Correct:

There are 4 conversion period not two.

**Multiple Choice Questions**

**Choose the correct answer from the given four options (3 to 9):**

Question 3.

The compound interest on ₹ 1000 at 10% p.a. for 2 years is

(a) ₹190

(b) ₹210

(c) ₹1210

(d) ₹200

Solution:

Principal (P) = ₹1000

Rate (R) = 10% p.a.

Period (n) = 2 years

and C.I. = A – P

= ₹1210 – ₹1000 = ₹210 (b)

Question 4.

The compound interest on ₹5000 at 20% per annum for \(1 \frac{1}{2}\) years compounded half yearly is

(a) ₹6655

(b) ₹1655

(c) ₹50

(d) ₹1000

Solution:

Principal (P) = ₹5000

Rate (R) = 20% p.a. or 10% half-yearly

Period (n) = \(1 \frac{1}{2}\) years or 3 half-years

∴ C.I. = A – P = ₹6655 – ₹5000 = ₹1655 (b)

Question 5.

The compound interest on ₹10000 at 8% per annum for 6 months compounded quarterly is

a) ₹408

(b) ₹10404

(c) ₹404

(d) ₹400

Solution:

Principal (P) = ₹ 10000

Rate (R) = 8% p.a. or 2% quarterly

Period (n) = 6 months = 2 quarters

∴ C.I. = A – P = ₹10404 – ₹10000 = ₹404 (b)

Question 6.

The time periods and rate for a sum taken at 8% p.a. for \(1 \frac{1}{2}\) years compounded half yearly are

(a) n = 3, R = 4%

(b) n = 6, R = 2%

(c) n = 3, R = 2%

(d) n = 6, R = 4%

Solution:

Rate (R) = 8% p.a. = 4% half-yearly

Time (n) = \(1 \frac{1}{2}\) years = 3 half-year (a)

Question 7.

If ₹12000 taken for 2 years at 4% per annum compounded quarterly, then time period and rate is

(a) n = 2, R = 16%

(b) n = 4, R = 1 %

(c) n = 8, R = 1%

(d) n = 8, R = 16%

Solution:

Principal (P) = ₹ 12000

Rate (R) = 4% p.a. or 1% quarterly

Time (n) = 2 years or 8 quarter (c)

Question 8.

If the number of conversion periods ≥ 2, then compound interest is

(a) less than or equal to simple interest

(b) greater than or equal to simple interest

(c) less than simple interest

(d) greater than simple interest

Solution:

Number of conversion period ≥ 2

The C.I. is greater than simple interest (S.I.) (d)

Question 9.

The time in which ₹6000 amounts to ₹7986 at 10% p.a. compounded annually is

(a) 2 years

(b) 3 years

(c) 4 years

(d) 5 years

Solution:

Amount (A) = ₹7986

Principal (P) = ₹6000

Rate (R) = 10% p.a.

∴ n = 3

∴ Time = 3 years

**Value Based Question**

Question 1.

A person wants to invest ₹ 100000 in fixed deposit scheme for 2 years. His financial advisor explained him two type of schemes first is yielding 10% p.a. compounded annually, second is yielding 10% p.a. compounded semi-annually. Which scheme is better and why? Why investment is important for future life?

Solution:

Principal (P) = ₹ 100000

Rate = 10% p.a. or 5% per half-yearly

Period (n) = 2 years or 4 half-years

If interest is compounded half-yearly, then

It is clear that second scheme is more benificial.

For our future, we should save some money and

if possible we should invest it in some benificial schemes.

**Higher Order Thinking Skills (Hots)**

Question 1.

A certain sum of money is invested at the rate of 5% per annum compound interest, the interest compounded annually. If the difference between the interests of third year and first year is ₹102.50. Find the sum.

Solution:

Let sum of money = ₹100

Rate (R) = 5% p.a.

Question 2.

The difference between the compound interest and the simple interest on ₹42000 for two years is ₹105 at the same rate of interest per annum. Find

(i) the rate of interest

(ii) the compound interest earned in second year.

Solution:

Let P be the interest

Principal = ₹42000

Time 2 years

It is given that the difference between the compound interest

and the simple interest of ₹42000 for two years is ₹105.