**Simple Interest** : Interest refers to the monetary compensation that the borrower pays to the lender in exchange for utilizing the borrowed funds. The sum lent is called the principal. Interest is usually calculated at the rate of so many rupees for every 100 of the money lent for a year. This is called the rate percent per annum.

‘Per annum’ means for a year. The words ‘per annum’ are sometimes omitted. Thus, 6 p.c. means that 6 is the interest on 100 in one year.

The total obtained by adding the principal and interest together is referred to as the amount..

The interest is usually paid yearly, half-yearly or quarterly as agreed upon.

Interest is of two kinds, Simple and Compound. When interest is calculated on the original principal for any length of time it is called simple interest. Compound interest is defined in the next chapter.

To find Simple Interest, multiply the principal by the number of years and by the rate per cent and divide the result by 100. This may be remembered in the symbolic form

SI = p x t x r / **100**

Wherever I = interest, p = principal, t = number of years, r = rate %

Ex.1. Find the simple interest on 400 for 5 years at 6 percent.

Soln. SI = 400×5×6 / 100

= Rs 120

**Interest for a number of days**

In the case where time is measured in days or years and days, a year is considered to have 365 days. However, when time is measured in months and days, a year is considered to have 12 months and each month is assumed to have 30 days. It is important to note that when calculating the repayment date, the day on which the money is paid back should be included, while the day on which it is borrowed should be omitted.

Ex.2: Find the simple interest on 306. 25 from March 3rd to July 27^{th} at 3 3/3 % per annum.

Sol. Interest = Rs 3061/4 X146/365 X15/4 X1/100

= Rs 1225/4 X 2/5 X 15/4 X1/100 = rs 147/32

= 4.59 (nearly)

Note: 73, 146, 219 and 292 days are respectively 1/5,2/5,3/5 and 4/5 of a year.The interest I on principal P for d days at r p.c. is given by

I = P X r X d/365 X 1/100 = P X d X 2r/73000

Therefore, we can infer the subsequent guideline for computing the overall interest on varying principals for distinct durations, while maintaining a consistent interest rate in every scenario.

Rule. Calculate the total by multiplying each principal by its respective number of days, and then determine the sum of these products. Next, multiply this sum by twice the rate and divide the resulting product by 73000.

The 4 numbers intricate in questions linked with interest are P, t, r and I. If any three of these be given, the fourth can be found.

To find principal

Since I = ptr/100

Ex.3: What sum of money will produce 143 interest in 3 ¼ years 2 ½ p.c. simple interest?

Sol. Let the required sum be P. Then

Rs P= Rs 100×143 / 3 ¼ X 2 ½ = Rs 100 X 143 X 4 X 2 / 13 X5 = Rs 1760

To find rate %

Since I = Prt / 100

Ex.4: A sum of 468.75 was lent out at simple interest and at the end of year 8 months the total amount was 500. Find the rate of interest per cent per annum.

Sol. Here, P = 468.75, t = 1 2/3 or 5/3 years

I= (500-468.75) = 31.25

Ex. 5: A lent 600 to B for 2 years, and 150 to C for 4 years and received altogether 90 from both as interest. Treasure the amount of interest, simple interest being intended.

Sol. 600 for 2 years = 1200 for 1 year

and 150 for 4 years = 600 for 1 year

Int.=90

4011

Rate= 90 X 100 / 1800 X 1 = 5%

Ex.6: In what time will ₹8500 amount to 15767.50 at 4 ½ percent per annum?

Sol. Here, interest = 15767.50 – 8500 = 7267.50

T = 7267.50 X 100 / 8500 X 4.5

=19 years

Ex.7: The simple interest on a sum of money is 1/9 of the principal, and the number of years is equal to the rate percent per annum. Find the rate percent.

Soln: Let amount = P, time = t years, rate = t

Then, Ptt / 100 = P/9

t2 = 100/9

t = 10/3 = 3 1/3%

Ex.8: What annual payment will discharge a debt of 770 due in 5 the rate of interest being 5% per annum?

Soln: Let the annual payment be P rupees.

The amount of P in 4 years at 5% = 100+4x5P /100 = 120 P/100

” ” ” 3 yrs ” ” = 115 p / 100

” ” ” 2 yrs ” ” = 110p / 100

” ” ” 1 yrs ” ” = 105p / 100

These 4 quantities composed with the last annual payment of P will release the liability of 770.

120p / 100 + 115p / 100 + 110p / 100 + 105p / 100 + p = 770

550p / 100 = 770 p = 770 X 100 / 550 = 140

Hence, annual payment = 140

Theorem: The annual payment that will discharge a debt of A due in t years at the rate of interest r% per annum is

100A / 100t + rt(t-1) /2

Ex.9: What annual payment will discharge a debt of 848 in 4 yrs at 4% per annum?

Soln: By the theorem:

Annual payment = 848×100 / 4×100 + 4(3)(40 / 2 = Rs 200

Ex. 10: The annual payment of 80 in 5 years at 5% per annum simple interest will discharge a debt of

Soln: Stroking the morals in the above formula:

80 = Ax100 / 5×100 + 5(4)(5) / 2

or, A= 80×550 / 100

= Rs 440

Ex.11: The rate of interest for the first 2 yrs is 3% per annum, for the next 3 years is 8% per annum and for the period beyond 5 years 10% per annum. If a man gets 1520 as a simple interest for 6 years, how much money did he deposit?

Soln : Let his sum be = 100

Interest for first 2 yrs = 6

Interest for next 3 yrs = 24

Interest for the last year = 10

Total interest = 40

When interest is ₹40, deposited amount is ₹100.

when interest is 1520, deposited amount

100 / 40 x 1250 = Rs 3800