Answer :
Suppose a sum of Rs. 10000 is taken on loan at 10% per annum.
What will be interest payable in three years?
There are two ways in which interest may be paid.
(1). You pay interest every year on Rs. 10000 at 8% .
(i) So interest for 1st year = (10000x10)/100 = 1000
(ii) interest for 2nd year = (10000x10)/100 = 1000
(iii) interest for 3rd year = (10000x10)/100 = 1000
Hence total interest you pay for three years = 3000.
(2). (i) You pay interest for 1st year = (10000x10)/100 = 1000
(ii) Now in the 2nd year, you pay interest on Rs 10000 and also on Rs.1000 ,that is, you pay interest on original sum + Interest = interest on 11000. Hence interest for 2nd year = (11000x10)/100 = 1100.
(iii) Now in third year, you pay interest on original sum Rs10000 + interest for 1st years + interest for 2nd year = interest on 10000 + 1000 + 1100 = 12100.
Hence interest for third year = (12100x10)/100 = 1210
Hence total interest = 1000 + 1100 + 1210 = Rs.3310
You will observe that in the first case, equal interest has been paid every year.
In the second case, interest has been charged again on the interest for the previous years in addition to interest on the original sum. This method of computing interest is called compound interest.
What will be interest payable in three years?
There are two ways in which interest may be paid.
(1). You pay interest every year on Rs. 10000 at 8% .
(i) So interest for 1st year = (10000x10)/100 = 1000
(ii) interest for 2nd year = (10000x10)/100 = 1000
(iii) interest for 3rd year = (10000x10)/100 = 1000
Hence total interest you pay for three years = 3000.
(2). (i) You pay interest for 1st year = (10000x10)/100 = 1000
(ii) Now in the 2nd year, you pay interest on Rs 10000 and also on Rs.1000 ,that is, you pay interest on original sum + Interest = interest on 11000. Hence interest for 2nd year = (11000x10)/100 = 1100.
(iii) Now in third year, you pay interest on original sum Rs10000 + interest for 1st years + interest for 2nd year = interest on 10000 + 1000 + 1100 = 12100.
Hence interest for third year = (12100x10)/100 = 1210
Hence total interest = 1000 + 1100 + 1210 = Rs.3310
You will observe that in the first case, equal interest has been paid every year.
In the second case, interest has been charged again on the interest for the previous years in addition to interest on the original sum. This method of computing interest is called compound interest.
Compound interest
If money in a bank account has earned interest, the bank should compute the interest due, add it to the principal, and then pay interest on this new, larger amount. This in fact the way most bank accounts work. Interest that is paid on principal plus previously earned interest is called compound interest.
If the interest is added yearly, we say that the interest is compounded annually
If the interest is added every three months, we say that the interest is compounded quarterly
Interest also can be compounded monthly and daily
In order to reduce current taxes, he has agreed to defer a $15 million bonus to be paid as $18 million 4 years from now. If the heat invests the $15 million now, what is the minimum annual interest rate they need to earn to guarantee that the $18 million is available in 4 years? Assume that the annual interest is compounded monthly
To solve the compound interest problem, we will use the formulae A=P(1+(r/m))^n
with A=18,P=15,m=12 and n=12*4=48
we will solve for r
substituing A,P,m and n we solve as follows
18=15(1+(r/12))^48
dividing both sides by 15
1.2=(1+(r/12))^48
raise both sides to the 1/48th power
(1.2)^1/48=((1+(r/12))^48)^1/48
(1.2)^1/48=1+r/12
adding -1 on both sides
r/12=(1.2)^1/48-1
r/12=1.003805589-1=0.003805589
r=12*0.003805589
=0.046
thus the heat needs to find an investment that pays about 4.6% annual interest rate monthly
If money in a bank account has earned interest, the bank should compute the interest due, add it to the principal, and then pay interest on this new, larger amount. This in fact the way most bank accounts work. Interest that is paid on principal plus previously earned interest is called compound interest.
If the interest is added yearly, we say that the interest is compounded annually
If the interest is added every three months, we say that the interest is compounded quarterly
Interest also can be compounded monthly and daily
In order to reduce current taxes, he has agreed to defer a $15 million bonus to be paid as $18 million 4 years from now. If the heat invests the $15 million now, what is the minimum annual interest rate they need to earn to guarantee that the $18 million is available in 4 years? Assume that the annual interest is compounded monthly
To solve the compound interest problem, we will use the formulae A=P(1+(r/m))^n
with A=18,P=15,m=12 and n=12*4=48
we will solve for r
substituing A,P,m and n we solve as follows
18=15(1+(r/12))^48
dividing both sides by 15
1.2=(1+(r/12))^48
raise both sides to the 1/48th power
(1.2)^1/48=((1+(r/12))^48)^1/48
(1.2)^1/48=1+r/12
adding -1 on both sides
r/12=(1.2)^1/48-1
r/12=1.003805589-1=0.003805589
r=12*0.003805589
=0.046
thus the heat needs to find an investment that pays about 4.6% annual interest rate monthly