Math CentralQuandaries & Queries


Question from maninder, a student:

at what rate % compound interest per annum will be rs. 640 amount to rs. 774.40 in 2 years.


Let's suppose for example that you invested rs. 640 for two years at 8% per year compounded annually. I want to write the interest rate r as a decimal fraction so r = 0.08. At the end of the first year the value of your investment is

rs. 640 + 0.08 × 640 = 640(1 + 0.08)

This is the amount that you invest for the second year and hence the value of your investment at the end of the second year is

640(1 + 0.08) + 0.08 × 640(1 + 0.08) = 640(1 + 0.08)( 1 + 0.08) = 640(1 + 0.08)2

I am not going to do the arithmetic because it's the form of the expression I want you to notice. For your problem you know that this value is rs. 774.40 but you don't know the interest rate r. In the expression above replace 0.08 by r and set it equal to 774.40. Solve for r.

I hope this helps,

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