# Rs 1600 lent at a compound interest of 5% per annum, compounded half yearly for one year will amount to

(a) Rs 1640

(b) Rs 1680

(c) Rs 1681

(d) Rs 1764

**Solution:**

The problem concerns the concept of compounding the formula for which is given by:

Amount = Principal(1 + r/100)^{n}

Where

r = rate of interest for the given period (years, months, days etc)

n = time period for which the compounding takes place

In the given problem the interest is compounded half yearly and therefore

r = 5/2 = 2.5% half yearly

And

n = 2(because there two period of six months each in a year)

Principal = Rs. 1600

Amount = 1600(1 + 2.5/100)^{2}

= 1600(1 + 0.025)^{2}

= 1600(1.025)^{2}

= 1600(1.050625)

= Rs. 1681

**✦ ****Try this: **Rs 1600 lent at a compound interest of 5% per annum, compounded annually for one year will amount to?

In the given problem the interest is compounded half yearly and therefore

r = 5% per annum

And

n = 1 year

Principal = Rs. 1600

Amount = 1600(1 + 5/100)^{1}

= 1600(1 + 0.05)^{1}

= 1600(1.05)

= Rs. 1680

**☛ Also Check: **NCERT Solutions for Class 8 Maths Chapter 8

**NCERT Exemplar Class 8 Maths Chapter 9 Sample Problem 4**

## Rs 1600 lent at a compound interest of 5% per annum, compounded half yearly for one year will amount to (a) Rs 1640, (b) Rs 1680, (c) Rs 1681, (d) Rs 1764

**Summary:**

Rs 1600 lent at a compound interest of 5% per annum, compounded half yearly for one year will amount to Rs. 1681

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