Time Value of Money

Concept:Simple interest with a withdrawal: interest is earned on the amount that remains in the account after withdrawal.Explanation:Let the rate be $r\%$ per annum.Interest for first 2 years on Rs. 10,000:$SI_1 = \frac{10000 \times r \times 2}{100} = 200r$.Amount after 2 years = $10000 + 200r$.Withdrawal of Rs. 4,000 reduces this to:New principal = $10000 + 200r - 4000 = 6000 + 200r$.Interest for next 3 years on this new principal:$SI_2 = \frac{(6000+200r) \times r \times 3}{100} = \frac{3r(6000+200r)}{100}$.Final amount after 5 years = new principal + $SI_2$ = Rs. 7,900:$(6000+200r) + \frac{3r(6000+200r)}{100} = 7900$.Factor: $(6000+200r)\left(1 + \frac{3r}{100}\right) = 7900$.Multiply out: $6000 + 180r + 200r + 6r^2 = 7900$$6r^2 + 380r + 6000 = 7900$$6r^2 + 380r - 1900 = 0$Divide by 2: $3r^2 + 190r - 950 = 0$.Solve: $r = \frac{-190 \pm \sqrt{190^2 + 4\cdot3\cdot950}}{2\cdot3} = \frac{-190 \pm \sqrt{36100 + 11400}}{6} = \frac{-190 \pm \sqrt{47500}}{6}$.$\sqrt{47500} \approx 217.945$, so positive root = $\frac{27.945}{6} \approx 4.6575\%$.This rate is not among 5%, 6%, or 10%.Answer:The rate of simple interest is none of the given options.