15000 is deposited at simple interest. If the amount after 8 years is rs 25800, find the rate of interest
Answers
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
Use the formula of simple intereste
SI = P×R×T/100
And you will get rate is 21.5