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Find the Amount and the Compound Interest on Rs 10,000 for `1 1/2` Years at 10% per Annum, Compounded Half Yearly. Would this Interest Be More than the Interest He Would Get If It Was Compounded Annually? - Mathematics

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ConceptRate Compounded Annually Or Half Yearly (Semi Annually)

Question

Find the amount and the compound interest on Rs 10,000 for `1 1/2` years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?

Solution

P = Rs 10,000

Rate = 10% per annum = 5% per half year

n = `1 1/2` year

There will be 3 half years in `1 1/2` years.

A = Rs `[10000(1 + 5/100)^3] = Rs[10000(1 + 1/20)^3]`

= Rs `(10000 xx 21/20 xx 21/20 xx 21/20)` = Rs 11576.25

C.I. = A − P

= Rs 11576.25 − Rs 10000 = Rs 1,576.25

The amount for 1 year and 6 months can be calculated by first calculating the amount for 1 year using the compound interest formula, and then calculating the simple interest for 6 months on the amount obtained at the end of 1 year.

The amount for the first year has to be calculated first

A =  Rs `[10000(1 + 10/100)^1] = Rs[10000(1 + 1/10)]`

= Rs `(10000 xx 11/10)`= Rs 11000

By taking Rs 11,000 as the principal, the S.I. for the next `1/2` year will be calculated.

S.I. = Rs `((11000xx10xx1/2)/100)` = Rs 550

∴ Interest for the first year = Rs 11000 − Rs 10000 = Rs 1,000

∴ Total compound interest = Rs 1000 + Rs 550 = Rs 1,550

Therefore, the interest would be more when compounded half yearly than the interest when compounded annually.

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APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 8 (2018 to Current)
Chapter 8: Comparing Quantities
Ex. 8.3 | Q: 8 | Page no. 134

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Solution Find the Amount and the Compound Interest on Rs 10,000 for `1 1/2` Years at 10% per Annum, Compounded Half Yearly. Would this Interest Be More than the Interest He Would Get If It Was Compounded Annually? Concept: Rate Compounded Annually Or Half Yearly (Semi Annually).
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