Find the amount which ram will get on rs. 4096,if he gave it for 18 months at 12½% per annum, interest being compounded half yearly.
Answers
Step-by-step explanation:
Given:-
Principle is Rs. 4096 , time is 18months compound interest is calculated half yearly at the rate of 12 1/2 %
To find:-
Find the amount which ram will get on rs. 4096,if he gave it for 18 months at 12½% per annum, interest being compounded half yearly.
Solution:-
Principle (P) = Rs. 4096
Time (T) = 18 months
We know that 1 year = 12 months
=>12 months = 1 year
=> 1 month = 1/12 years
=>18 months = 18/12 years
=>18 months = 3/2 years
=>18 months = 3×(1/2 ) years
Compound interest is calculated for half yearly then
Number of times the interest is calculated for 18 months = 3 times
=>n = 3
Rate of Interest (R) = 12 1/2%
=>R = 25/2%
Rate of interest is calculated for annum = 25/2%
Rate of interest is calculated for half year = (25/2)×(1/2)%
=>(25/4)%
We know that
The Amount (A)=P[1+(R/100)]^n
=>A = 4096×[1+{(25/4)/100}]^3
=>A = 4096×[1+(25/400)]^3
=>A = 4096×[1+(1/16)]^3
=>A = 4096×[(16+1)/16]^3
=>A = 4096×(17/16)^3
=>A = 4096×(4913/4096)
=>A =4913
Amount = Rs. 4913
Answer:-
Ram will get Rs. 4913 after 18 months at the rate of 12 1/2% per annum on Rs. 4096 when the compound interest is calculated half yearly.
Used formula:-
Amount (A)=P[1+(R/100)]^n
Where , A = Amount
P = Principle
R = Rate of interest
n = number of times the interest is calculated compounded.