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# Simple Interest

• Difficulty Level : Easy
• Last Updated : 07 Aug, 2019
• The amount which is lent / deposited is called Principal
• The money that the principal generates is called Interest. This is the money generated as a result of borrowing/lending.
• Simple Interest is the interest calculated on the Principal amount, rather than being calculated on cumulative amount.
• Simple Interest, SI = P x R x T / 100, where P is the principal, R is the rate of interest per unit time period and T is the time period.
• Final Amount = Principal + SI

### Sample Problems

Question 1 : What would be the annual interest accrued on a deposit of Rs. 10,000 in a bank that pays 4 % per annum rate of simple interest ?
Solution : Here, P = 10000, R = 4, T = 1
=> SI = P x R x T / 100
=> SI = 10000 x 4 x 1 / 100
=> SI = 400
Thus, the annual interest would be Rs. 400

Question 2 : A sum of money amounts to Rs. 28,000 in 2 years at 20 % simple interest per annum. Find the sum.
Solution : Here, A = 28000, T = 2, R = 20
=> A = P + SI
=> A = P + (P x R x T / 100)
=> A = P [1 + (R x T / 100)]
=> 28000 = P [1 + 0.4]
=> P = 28000 / 1.4
=> P = 20000
Thus, the required sum is Rs. 20,000

Question 3 : A man borrowed a certain sum of money at the rate of 6 % per annum for the first two years , 9% per annum for the next three years, and 14% per annum for the period beyond 5 years. If he pays a total interest of Rs. 22,800 at the end of 9 years, find the amount he borrowed.
Solution : Let the borrowed sum be P.
=> SI for first 2 years + SI for next 3 years + SI for next 4 years = 22800
=> (P x 6 x 2 / 100) + (P x 9 x 3 / 100) + (P x 14 x 4 / 100) = 22800
=> 95 P / 100 = 22800
=> P = 24000
Therefore, Borrowed sum = Rs. 24,000

Question 4 : At what annual rate of interest will a sum of money be thrice in 10 years?
Solution : Amount = Principal + SI
If the sum of money would be thrice the principal after 10 years, the SI would be twice the principal.
=> SI = 2 x P
=> (P x R x T / 100) = 2 X P
=> R x T / 100 = 2
=> R x T = 200
=> R x 10 = 200
=> R = 20 %
Thus, the required rate of interest is 20 %

Question 5 : The simple interest on a sum of money in 5 years at 12 % per annum is Rs. 400 less than the simple interest accrued on the same sum in 7 years at 10 % per annum. Find the sum.
Solution : Let the sum be P.
=> SI in 5 years at 12 % per annum = P x 12 x 5 / 100 = 0.6 P
=> SI in 7 years at 10 % per annum = P x 10 x 7 / 100 = 0.7 P
Now, according to the question,
0.7 P – 0.6 P = 400
=> 0.1 P = 400
=> P = 4000
Thus, the required sum is Rs. 4000

Question 6 : A sum of Rs. 1000 was lent to two people, one at the rate of 5 % and other at the rate of 8 %. If the simple interest after one year is Rs. 62, find the sum lent at each rate.
Solution : Let the sum lent at 5 % be P.
=> Sum lent at 8 % = 1000 – P
Now, according to the question,
SI for 5 % + SI for 8 % = 62
=> (P x 5 x 1 / 100) + ((1000 – P) x 8 x 1 / 100) =62
=> 5 P + 8 (1000 – P) = 6200
=> 5 P + 8000 – 8 P = 6200
=> 3 P = 1800
=> P = 600
Therefore, sum lent at 5 % = P = Rs. 600
Sum lent at 8 % = 1000 – P = Rs. 400