Important Questions On Simple Interest and Compound Interest

By PARUL RISHI|Updated : May 1st, 2023

Important Questions On Simple Interest and Compound Interest. In the previous articles, we have studied the basic concepts and types of questions that are asked in the exam. In this article, we will discuss the questions which are important for the upcoming exam.

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Question. A certain sum of money at simple interest works out to Ps. 1012 in 2.5 years and to Rs. 1067.20 in 4 years. Then find the rate of interest?

Solution:

Amount, A = P + S I for 2 ½ years = Rs.1012
Amount for 4 years = Rs.1067.20.
Therefore, S I for 1 ½ years = Rs.1067.20 – Rs.1012 = Rs.55.20
So, S I for 2 ½ years = 55.20 ÷ 3/2 × 5/2 = 55.20 × 2/3 × 5/2 = Rs.92.
Therefore, the Principal = Amount – S I = 1012 – 92 = Rs.920.
The rate of interest = SI × 100/P n
= 92 × 100/920 × 5/2 = 92 × 100 × 2 / 920 × 5 = 4%

Question. A certain amount of money at r% compounded annually after two and three years becomes Rs. 1440 and Rs. 1728 respectively. Then find the value of r.

Solution:

I the principal be Rs. P, then

On dividing equation (ii) by (i),

= 20% per annum

Short Trick:
Subtract the amount of 2yrs from the amount of 3 yrs
1728 - 1440 = 288
= 288x100/1440 = 20%
Question. If a man receives simple interest on one-fourth of his capital 3% interest, on two third 5% and on the remainder 11%, then find the percentage he receives on the whole in a year for the complete amount?

Solution:

Let the total capital be x

Total interest per annum=x/4 × 3/100+ 2x/3 × 5/100 + x/12 × 11/100
=x/20
If R is the rate of interest R=x/20 × 100/x=5%

Question. A bank gives compound interest on deposits at the rate of 5% for the first year, 6% for the second year and 10% for the third year. If a deposit amounts to ₹12,243 at the end of the third year, then what was the initial deposit?

Solution:

If the principal be ₹P, then Amount

=
=

= ₹10000

Question.Find the time in which 80,000 amounts to 92,610 at 10% p.a. at compound interest, interest being compounded semiannually?

Solution:

Formula for calculating amount is as follows:-
A = P(1 + r/n)^nt where;
•A = Accrued Amount (principal + interest) = Rs 92610
•P = Principal Amount = Rs 80000
•R = Annual Nominal Interest Rate in percent = 10%
•r = R/100
•t = Time Involved in years, 0.5 years is calculated as 6 months, etc.
•n = number of compounding periods per unit t; at the END of each period = 2(compounded semi annually)
Thus; 92610 = 80000(1 + 10/200)^2t;
After calculating we get the value of t as 1.5 years.

Question. At a certain rate of simple interest, a certain sum of money becomes double of itself in 10 years. After how many years it will treble itself ?

Solution :

Let the principal be Rs x
Amount = Rs. 2x
SI = 2x – x = Rs. x

Case II
Rate = 10%
Principal = Rs. x
Amount = Rs. 3x
SI = 3x – x = 2x