Page 136 - Start Up Mathematics_7

(iii) Amount: The total sum of money including the principal and the interest is called amount.

Amount = Principal + Interest

(iv) Rate of interest: The fixed percentage at which interest is calculated for a certain period
of time, usually on yearly basis is called rate of interest.

(v) Time period: The period for which the money is borrowed or given is known as time period.
(vi) Simple interest: The interest calculated uniformly on the original principal throughout the

loan period is called simple interest.
Let principal be ` P, rate of interest be R% p.a. and time be T years.

Principal × Rate× Time P × R × T
Then, Simple Interest (S.I.) = =
100 100

S.I. × 100 S.I × 100 S.I × 100
Also, P = R = T =
R × T P × T P × R

Example 22: Find the amount to be paid at the end of 4 years if principal is ` 1,200 at 10% p.a.
Solution: Principal = ` 1,200 Rate = 10% p.a. Time = 4 years

P × R × T , 1 200 10 4× ×
S.I. = = = ` 480
100 100
∴ Amount to be paid after 4 years = Principal + S.I. for 4 years
= ` 1,200 + ` 480 = ` 1,680
Example 23: Sandeep borrowed ` 6,000 from his friend and returned ` 7,500 to him after one
year. Calculate the rate percent.

Solution: Principal = ` 6,000, Amount = ` 7,500, Time = 1 year
S.I. = Amount – Principal = ` 7,500 – ` 6,000 = ` 1,500

S.I × 100 1,500 × 100
R = = = 25%
P × T 6,000 × 1
Example 24: The simple interest on a certain sum of money for 5 years at 10% p.a. is ` 880 more
than the simple interest on the same sum at 7% p.a. for 4 years. Find the sum.

Solution: Let’s assume the principal in each case = ` 100
100 × 10 × 5
S.I. for 5 years at 10% p.a. = = ` 50
100
100 × 7 × 4
S.I. for 4 years at 7% p.a. = = ` 28
100

Difference in interest = ` 50 – ` 28 = ` 22
If the difference in interest is ` 22, then the principal = ` 100

100
If the difference in interest is ` 880, then the principal = × 880 = ` 4,000
22
∴ The principal invested is ` 4,000.

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