Simple Interest - Key Formulas
Basic Simple Interest Formula
To calculate simple interest:
Where:
SI = Simple Interest
P = Principal (initial amount)
R = Rate of interest per annum (%)
T = Time period (in years)
Amount Calculation
To calculate the final amount:
Where:
A = Final amount
P = Principal
SI = Simple Interest
Finding Principal
To find the principal amount:
This is useful when you know the interest earned and need to find the initial investment.
Finding Rate of Interest
To find the rate of interest:
This helps determine the interest rate when other values are known.
Simple Interest Problems
Practice aptitude questions on simple interest calculations
Question 1:
What will be the simple interest on Rs. 80,000 at 16(2/3) % per annum for 9 months?
We are given:
1) Principal = Rs. 80,000
2) Rate of interest = 16(2/3)% = 50/3%
3) Time = 9 months = 3/4 years
Simple Interest = (P × R × T) / 100
Substituting the given values, we get
Simple Interest = (80,000 × 50/3 × 3/4) / 100
Simple Interest = Rs. 10,000
Question 2:
Find the simple interest on Rs. 5000 at 6% per annum for the period from 5th Feb to 19th April, 2015.
We are given:
1) Principal = Rs. 5000
2) Rate of interest = 6%
3) Time = 5th Feb to 19th April, 2015
First find the time period 5th Feb to 19th April, 2015
Feb = 28 – 5 = 23 days
March = 31 days
April = 19 days
Total days = 23 + 31 + 19 = 73 days
Convert days into years, by dividing it by 365
Time = 73/365 = 1/5
Simple Interest = (P × R × T) / 100
= [5000 × 6 × (1/5)] / 100
= Rs. 60
Question 3:
A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 × 3) = Rs. 117.
Principal = Rs. (815 - 117) = Rs. 698.
Question 4:
Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?
Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 - x).
Then, [x × 14 × 2]/100 + [(13900 - x) × 11 × 2]/100 = 3508
28x - 22x = 350800 - (13900 × 22)
6x = 45000
x = 7500.
So, sum invested in Scheme B = Rs. (13900 - 7500) = Rs. 6400.
Question 5:
A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?
Principal = (100 × 4016.25) / (9 × 5)
= 401625 / 45
= Rs. 8925
Question 6:
How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
Time = (100 × 81) / (450 × 4.5) years = 4 years
Question 7:
Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
Let rate = R% and time = R years.
Then, (1200 × R × R) / 100 = 432
12R² = 432
R² = 36
R = 6
Question 8:
A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?
S.I. = Rs. (15500 - 12500) = Rs. 3000.
Rate = (100 × 3000) / (12500 × 4)% = 6%
Question 9:
An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:
Let the sum be Rs. 100. Then,
S.I. for first 6 months = Rs. (100 × 10 × 1) / (100 × 2) = Rs. 5
S.I. for last 6 months = Rs. (105 × 10 × 1) / (100 × 2) = Rs. 5.25
So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs. 110.25
Effective rate = (110.25 - 100) = 10.25%
Question 10:
A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:
Let the rate be R% p.a.
Then, (5000 × R × 2) / 100 + (3000 × R × 4) / 100 = 2200
100R + 120R = 2200
R = 2200 / 220 = 10
Rate = 10%
Question 11:
A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:
Principal = (100 × 5400) / (12 × 3) = Rs. 15000
Question 12:
A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:
S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205.
S.I. for 5 years = Rs. (2205 / 3) × 5 = Rs. 3675
Principal = Rs. (9800 - 3675) = Rs. 6125.
Hence, rate = (100 × 3675) / (6125 × 5)% = 12%
Question 13:
What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years?
Let the principal be P and rate of interest be R%.
Required ratio = (P × R × 6) / 100 : (P × R × 9) / 100
= 6PR : 9PR
= 6 : 9
= 2 : 3
Question 14:
A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6% p.a for 2 years. Find his gain in the transaction per year.
Gain in 2 years = Rs. (5000 × 6 × 2) / 100 - (5000 × 4 × 2) / 100
= Rs. (600 - 400)
= Rs. 200
Gain in 1 year = Rs. 200 / 2 = Rs. 100
Question 15:
A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?
Let the principal be Rs. P and rate be R%.
Then, (P × R × 7) / 100 = 1750
PR = 25000 / 7
Now, additional interest = [P × 2 × 7] / 100
= 14P / 100
= 14 × 25000 / (100 × 7)
= 350000 / 1000
= Rs. 350