Question

Bank A offers 6% interest rate per annum compounded half yearly. Bank B and Bank C offer simple interest but the annual interest rate offered by Bank C is twice that of Bank B. Raju invests a certain amount in Bank B for a certain period and Rupa invests ₹ 10,000 in Bank C for twice that period. The interest that would accrue to Raju during that period is equal to the interest that would have accrued had he invested the same amount in Bank A for one year. The interest accrued, in INR, to Rupa is

Accepted Answer

A. In Bank A, effective interest rate for 1 year compounded half yearly at 6% p.a. (3% per half-year): $$	ext{Effective rate} = (1.03)^2 - 1 = 0.0609 = 6.09\%$$ Raju's interest in Bank B for period $t$ at simple interest rate $r$ equals Bank A's 1-year interest: $$I_{Raju} = P_R \cdot r \cdot t = P_R 	imes 0.0609 \implies rt = 0.0609$$ Rupa invests ₹ 10,000 in Bank C at rate $2r$ for period $2t$: $$I_{Rupa} = 10000 	imes (2r) 	imes (2t) = 40000 	imes (rt)$$ $$I_{Rupa} = 40000 	imes 0.0609 = 2436$$.

Interest accrued to Rupa across banks

Explanation

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