Math, asked by deadketchum, 2 months ago

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

Answered by tennetiraj86
15

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.

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