Find the amount which Ram will get on ₹ 4,096, if he gave it for 18 months at 12an a half per annum, interest being compounded half yearly.
Answers
HEY MATE ,
Simple Interest
If the principal remains the same throughout the loan period then the interest calculated on this principle is called the simple interest.
Principal (P): The original sum of money loaned/deposited. Also known as capital.
Time (T): The duration for which the money is borrowed/deposited.
Rate of Interest (R): The percent of interest that you pay for money borrowed, or earn for money deposited
Simple interest is calculated as
S.I= (P×R×T)/100
Total amount at the end of time period
A= P + SI
Compound interest
The time Period after which interest is added each time to form a new principal is called the conversion period and the interest so obtained is called a compound interest.
If the conversion period is 1 year then the interest is said to be compounded annually.
The main difference between the simple interest and compound interest on a certain sum is that in the case of simple interest the principal remains constant throughout whereas in the case of compound interest it goes on changing periodically.
The above formula is the interest compounded annually
A= P(1+r/100)^n
Compound interest= A-P
Where A is the amount ,
P the principal,
r the rate percent per conversion period and n is the number of conversion
periods
Compound Interest Formula if the interest is compound half yearly
A= P(1+r/200)^2n
Here R/2 is the half yearly rate
2n is the number of half year
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Solution:
Given:
Principal (P)= ₹ 4096
Rate of interest(R) = 12 1/2% p.a = 25/2 %p.a
Time period = 18 months = 18 /12= 3/2 years
A = P(1 + R/200)^2n [for half yearly]
A = 4096 (1 + 25/ 2 x200)^3/2 x2
A = 4096 (1 + 25/400)^3
=4096(1 + 1/16)
= 4096(17/16)^3
= 4096( (17 x17 x 17 ) / (16 x 16 x16))
=4096( (17 x17 x 17 ) / (256 x16))
= 4096( (17 x17 x 17 ) / (4056))
= 17 x17 x17 = 289 x 17
A=₹ 4913
Hence Ram will get ₹ 4913 after 18 months.
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Hope this will help you...