# A sum of Rs 12,800 earns Rs 2017.60 in 18 months, when the rate of interest is reckoned half yearly. Find the rate.

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by lkrajani

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by lkrajani

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R = 12800 (1 + r )^n

this is compound interest situation. Since r is compounded half yearly. Let us take the interest at half yearly basis. r is interest per 6 months. in 18 months, we have half years. So interest is compoinded 3 times. so n = 3

R = 12800 + 2017.60 = principal + interest = Rs 14817.60

So 14817.60 = 12800 (1+r)³ so (1+r)³ = 14817.60 / 12800

So 1 + r = 1.05 => r = 0.05 => r = 5 %

Rate for 6 months is 5% .__ Rate per annum will be twice that is 10%.__

this is compound interest situation. Since r is compounded half yearly. Let us take the interest at half yearly basis. r is interest per 6 months. in 18 months, we have half years. So interest is compoinded 3 times. so n = 3

R = 12800 + 2017.60 = principal + interest = Rs 14817.60

So 14817.60 = 12800 (1+r)³ so (1+r)³ = 14817.60 / 12800

So 1 + r = 1.05 => r = 0.05 => r = 5 %

Rate for 6 months is 5% .

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

R =

Since r is half yearly.

so we have to take the interest at half yearly basis. r is interest per 6 months. in 18 months, we have half years. So interest is 3 times.

so n = 3

R = 12800 + 2017.60 = Rs 14817.60

So 14817.60 = 12800 (1+r)³

so (1+r)³ = 14817.60 / 12800

So 1 + r = 1.05

=> r = 0.05

=> r = 5 %

Rate for 6 months is 5% so per annum = 2 x 5 = 10 %

Since r is half yearly.

so we have to take the interest at half yearly basis. r is interest per 6 months. in 18 months, we have half years. So interest is 3 times.

so n = 3

R = 12800 + 2017.60 = Rs 14817.60

So 14817.60 = 12800 (1+r)³

so (1+r)³ = 14817.60 / 12800

So 1 + r = 1.05

=> r = 0.05

=> r = 5 %

Rate for 6 months is 5% so per annum = 2 x 5 = 10 %