Question

If the Principal(P) = ₹2500, Time (T) = 3years and Rate = 6% . Find the simple interest and Amount​

Answer 1

Answer:

Simple interest:-

Interest: The amount of money that you pay to borrow money or the amount of money that you earn on a deposit

Annual Interest Rate: The percent of interest that you pay for money borrowed, or earn for money deposited

General Information

S.I = PRT/100

1. Principle: The money borrowed or lent out for a certain period is called the principal or the sum (P).

2. Interest: The borrower pays a certain amount for the use of this money is called interest (S.I).

3. Time: The borrowing is for a specified period called Time (T).

4. Rate of interest: The specified term is expressed as percent of the principal is called rate of interest (R %).

5. Amount: The sum of the principal and the interest is called the amount or Future value.

Amount=principal+interest=P+PRT/100=P(1+RT/100)

Compound interest:-

When interest charged over a period of time is added up in the principal, the interest so charged on this new principal is called compound interest.

If P = sum or Principal

n = time in years

R = rate percent per annum

Then, amount = P(1+R/100)^n

(i) When interest is compounded half-yearly,

Amount = P(1+(R/2)/100)^2n

(ii) When interest is compounded quarterly,

Amount = P(1+(R/4)/100)^4n

(iii) When interest is compounded annually but time in fraction, say 21/5 years.

Amount = P〖(1+R/100)^2×(1+(R 1/5)/100)〗^1

(iv) When rates are different for different years, say R1%, R2%, and R3% for 1st, 2nd and 3rd year respectively then,

Amount = P(1+R1/100)(1+R2/100)(1+R3/100)

(v) Present worth of Rs. X due n years hence is given by:

Present worth = x/(1+R/100)^n

Very Important Formulae’s

The difference between the simple interest and compound interest for 2 year (or terms) is given by the formula

Difference = P(R/100)^2

The difference between the simple interest and compound interest for 3 year (or terms) is given by the formula

Difference = P[(R^2 (R+300))/〖100〗^3 ]

Concept of Equal Installments in Compound interest

P = X/(1+r/100)^n +X/(1+r/100)^((n-1)) +⋯………..+X/((1+r/100) )

P = Principal

X = installment

R = rate

N = number of years

Ex. 1. Robin lends Rs.9 to Rahul on the condition that the loan is repayable in 10 months in 10 equal installments of Re.1 each. Find the rate of interest per annum.

Sol. Let the rate of interest per month be r

Total amount repaid = Rs.10

Interest = Re.1

r/100(9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1) = 1

So r = 100/45

Hence, the rate of interest per annum = (100/45) 12 = 26 2/3%

Ex. 2. A milkman borrowed Rs. 2500 from two money lenders. For one loan, he paid 5% p.a. and for the other he paid 7% p.a. The total interest paid for two years was Rs. 265. How much did he borrow at 5% and how much at 7%?

Sol. Let the loan be Rs. x at 5% p.a and Rs (2500 – x) at 7% p.a.

Total interest for 2 years = ([X×5×2+(2500-X)×7×2])/100

Given simple interest for the total amount = Rs. 265

([X×5×2+(2500-X)×7×2])/100 = 265

Solving, we get x = 2125

Amount borrowed at 5% = Rs. 2125

Amount borrowed at 7% = Rs. 375

Ex. 3. Three persons Amar, Akbar and Anthony invested different amounts in a fixed deposit scheme for one year at the rate of 12% per annum and earned a total interest of Rs.3240 at the end of the year. If the amount invested by Akbar is Rs.5000 more than the amount invested by Amar and the amount invested by Anthony is Rs.2000 more than the amount invested by Akbar, what is the amount invested by Akbar?

Sol. P = Amar + Akbar + Anthony

= x + x + 5000 + x + 7000

= 3x + 12000

(3240×100)/2 = 3x + 12000

⇒ 27000 – 12000 = 3x

⇒ 15000 = 3x

⇒ x = 5000

Akbar = 5000 + 5000 = Rs.10000

Ex. 4.Vankatlal takes money from the Employees Cooperative Society at lower rate of interest and invests in a scheme, which gives him a compound interest of 20%, compounded annually. Find the least number of complete years after which his sum will be more than double.

Sol. Let P = Rs.100

After 4 years, the amount will be 100 x 1.2 x 1.2 x 1.2 x 1.2 = Rs. 207.3, which is more than the double of Rs. 100

Answer 2

${\red{\underline{\underline{\bold{Given:-}}}}}$

• Principal = ₹2500
• Time = 3 years
• Rate = 6%

${\blue{\underline{\underline{\bold{To\:Find:-}}}}}$

• Simple Interest
• Amount

${\green{\underline{\underline{\bold{Answer:-}}}}}$

Principal (P) = ₹2500 , Time = 3years and Rate = 6%

➡ Simple Interest (I) = $\frac{P×T×R}{100}$

= $\frac{2500\times 3\times 6}{100}$

= ₹450

➡ Amount = Simple Interest + Principal

= ₹2500+₹450

= ₹2950

${\orange{\underline{\underline{\bold{Required\:Answer:-}}}}}$

• Simple Interest = ₹450
• Amount = ₹2950

_________________

Formulas used here:-

• Simple Interest = $\frac{Principal×Time×Rate}{100}$
• I = $\frac{P×T×R}{100}$
• Amount = Principal + Simple Interest
• A = P + I

___________________

Additional Information:-

If Simple Interest (I) , Time ( T) and Rate (R) are given, the formula used for finding Principal(P) :-

• P = $\frac{I×100}{R×T}$

If Simple Interest (I) , Principal (P) and Rate (R) are given, the formula used for finding Time(T) :-

• T = $\frac{I×100}{P×R}$

If Simple Interest (I) , Principal (P) and Time (T) are given, the formula used for finding Rate ( R) :-

• R = $\frac{I×100}{P×T}$