**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

Where I = Interest, p = principle, t = number of years, r = % rate

**Ex. 1. **Find the simple interest on Rs.400 for 5 years at 6 per cent.

**Solution:**

**Interest for a number of days**

When the time is given in days or in years and days, 365 days are reckoned to a year. But when the time is given in months and days, 12 months are reckoned to a year and 30 days to the month. The day on which the money is paid back should be include be but not the day of which it is borrowed, ie, in counting, the first day is omitted.

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

Solution:

Interest = Rs.

= = Rs. 4.59

**To find the principal:**

Since I =

**Ex.3.** What sum of money will produce Rs.143 interest in 3(1/4) years at 2.50 p.c. simple interest?

**Solution:**

Let the required sum be Rs. P. Then

Rs P =

**To find rate %:-**

Since I =

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**Ex. 4.** A sum of Rs.468.75 was lent out at simple interest and at the end of 1 year 8 months the total amount was Rs500. Find the rate of interest per cent annum.

**Solution:**

Here, P =Rs468.75, t = or

I = Rs.(500-468.75) = Rs.31.25

rate p.c. =

**To find Time:-**

Since, I = P t r / 100

**Ex. 5.** In what time will Rs.8500 amount to Rs.15767.50 at per cent per annum?

**Solution:**

Here , interest = Rs.15767.50 – Rs.8500 =Rs.7267.50

**Miscellaneous Examples of Simple Interest:**

**Ex.6:** The simple interest on a sum of money is 1/9^{th} of the principal, and the number of years is equal to the rate per cent per annum. Find the rate per cent.

**Solution:**

Let principal = P, time = t year, rate = t

Then,

Hence, rate = %

**Direct formula:**

**Rate **= time = %

**Ex. 7:** 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. To fetch interest of 1520 in six years, money did he deposit?

**Solution**

Let his deposit be = Rs 100

Interest for first 2 yrs = Rs 6

Interest for next 3 yrs = Rs 24

Interest for the last year = Rs 10

Total interest = Rs 40

When interest is Rs 40, deposited amount is Rs 100

when interest is Rs 1520, deposited amount = = Rs 3800

**Direct formula:**

**Principle = Interest*100/r _{1}t_{1}+r_{2}t_{2}+r_{3}t_{3}…**

**= =Rs 3800**

** ****Ex.8:** A sum of money doubles itself in 10 years at simple interest. What is the rate of interest?

**Solution:**

Let the sum be Rs 100

After 10 years it becomes Rs 200

Interest = 200 - 100 = 100

Then, rate = =

**Direct formula:**

**Time × Rate = 100 (Multiple numbers of principal – 1)**

Or, Rate =

Using the above formula rate =

**Ex.9:** A sum was put at a certain rate for 2 yrs. Had it been put at a 3% higher rate, it would have fetched Rs 300 more. Find the sum.

**Solution:**

Let the sum be Rs x and the original rate be y% per annum. Then, new rate = (y+3) % per annum

xy +3x – xy =15,000 or, x =5000

Thus, the sum =Rs 5000

**Direct Methods: **

** = **

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