Interest Formula and Compound Interest Calculation
Mathematics Shortcut (Interest Formula and Compound Interest Calculation)
Topics: Techniques for calculating all the interest calculations
Formula: 1
When the values of principal, time and interest rate are given, then
Interest / Profit = (Principal x Time x Interest Rate) / 100
Question: What is the 2-year interest on 600 at 9.5% simple interest?
Solution:
Interest / Profit = (600 x 2 x 9.5) / 100
= 114
Formula: 2
When the interest, principal and interest rate are given, then –
Time = (Interest x 100) / (Principal x Interest Rate)
Question: In how much time will the profit of 500 be 100 taka at 5% interest rate?
Solution:
Time = (100 x 100) / (500 x 5)
= 4 years
Formula: 3
When interest is multiplied by principal and the interest rate is specified, then –
Time = (interest times principal – 1) / interest rate x 100
Question: At an annual interest rate of 10 percent, after how many years will a capital double in interest?
Solution:
Time = (2– 1) / 10 x 100
= 10 years
Formula: 4
When interest is multiplied by principal and the time is specified, then
Interest rate = (interest times principal – 1) / time x 100
Question: At what percentage of simple interest is a capital, will it triple in interest in 8 years?
Solution:
Interest rate = (3 – 1) / 8 x 100
= 25%
Formula: 5
When interest time and principal are given, then
Interest rate = (interest x 100) / (principal or principal x time)
Question: At what percentage annual interest rate will the interest on 400 for 5 years be 140 taka?
Solution:
Interest rate = (140 x 100) / (400 x 5)
= 7
★Technique – 1: When the values related to principal, time and interest rate are given, then-
Interest or profit = (principal x time x interest rate) / 100
Question: What is the interest on 600 for 2 years at 9.5% simple interest?
Solution: Interest or profit = (600 x 2 x 9.5) / 100 = 114
★Technique – 2: When interest, capital and interest rate are given then –
Time = (interest x 100) / (principal x interest rate)
Question: At 5% interest rate, in how much time will the profit of 500 be 100 taka?
Solution: Time = (100 x 100) / (500 x 5) = 4 years
★Technique – 3: When interest is multiplied by principal and interest rate is specified then –
Time = (interest times principal – 1) / interest rate x 100
Question: At an annual interest rate of 10, after how many years will a capital double in interest?
Solution: Time = (2– 1) / 10 x 100 = 10 years
★Technique – 4: When interest is multiplied by principal and time is specified, then
Interest rate = (interest times principal – 1) / time x 100
Question: If the simple interest rate is how much, then any capital will triple in 8 years if it is compounded?
Solution: Interest rate = (3 – 1) / 8 x 100 = 25%
★Technique – 5: When interest is given as time and principal, then
Interest rate = (interest x 100) / (principal or capital x time)
Question: At what annual rate of interest will the interest on 400 taka for 5 years be 140?
Solution: Interest rate = (140 x 100) / (400 x 5) = 7
★Technique – 6: When two principal and two time interest are given then –
Interest rate = (Total interest x 100)/ {(1st principal x 1st time) + (2nd principal x 2nd time) }
Question: If the total interest of 5 years of 200 and 6 years of 500 at simple interest is 320, what is the interest rate?
Solution: Interest rate = (320x 100)/ {(200 x 5) + (500 x 6) } = 8
★Technique -7: When the interest rate, time and interest are mentioned in the principal-
Principal or principal = (100 x interest principal) / {100 + (time x interest rate)}
Question: How much money at 8% annual simple interest will be 1036 taka at 6 years of interest?
Solution: Capital or principal = (100 x 1036) / {100 + (6 x 48)} = 700
★Technique – 8: When interest, time and interest rate are mentioned
Principal = (interest x 100)/ (time x interest rate)
Question: At an annual interest rate of 4, how much will be the interest of 6 years, which will be 84?
Solution: Capital = (84 x 100)/ (6x 4) = 350
★Technique – 9: When there are two interest rates and interest rate and income decrease,
Principal = reduced income x 100 / {(1st interest rate – 2nd interest rate) x time}
Question: As the interest rate decreased from 6% to 4%, the annual income of a person decreased by 20 taka. What is his principal amount?
Solution: Actual = 20 x 100 / {(6 – 4) x1 = 1000
Determining Compound Interest
Technique:
Add the interest rate given by year and divide the square of the rate by 100 and add the quotient to the sum of the rates and find the percentage of the total taka. The compound interest can be found only by finding the percentage of the total taka.
Example >What is the compound interest for 2 years at 12% on 2500?
Answer: Since the years are doubled, double the rate and square the rate and divide by 100. Then add the quotient to the sum of the rates, the diameter is done.
(12 + 12)
= 24 + 1.44
= 25.44% Suppose 636 compound interest on 2500.
Some numbers
- At what percentage annual interest rate will a principal be tripled in 25 years?
- At how many years will a principal be doubled in 25 years at an interest rate of 20?
Technique:
Subtract 1 from whatever is left, multiply by 100 and divide by the given rate to get the time. And if divided by the given year, then the rate will be found.
That is, the formula
rxt = (n-1)x100. ( Here r = percentage, t = time )
Now do the number 1
Given t=25, n =3 ; r=?
r= {(n-1)x100}/t
={(3-1)x100}25
={2×100}25
=200/25
=8 % (Answer)
Given t=?, n =2 ; r=20
t= {(n-1)x100}/r
={(2-1)x100}/20
=100/20
=5 years (Answer)
Do it yourself - At what rate of interest per cent per annum will a principal amount triple in 10 years?
- At what rate of interest per cent per annum will a principal amount double in 5 years?
- At what rate of interest per cent per annum will a principal amount triple in how many years?
- At what rate of interest per cent per annum will a principal amount quadruple in how many years?
Answer: 20%, 20%, 20y, 20y