The price of a T.V. set worth ₹ 20,000 is to be paid in 20 instalments of ₹ 1000 each. If the rate of interest be 6% per annum, and the first instalment be paid at the time of purchase, then the value of the last instalment covering the interest as well will be :

### Concept & Logic In instalment schemes where the interest is accumulated and paid at the very end, the interest is calculated on the outstanding principal balance month by month. $$SI = \frac{P \times R \times T}{100}$$ ### Step-by-Step Solution * **Given:** Cash price = ₹ 20,000. First instalment paid at purchase = ₹ 1000. * Outstanding loan amount initially = $20,000 - 1,000$ = ₹ 19,000. * This remaining amount is paid in 19 equal monthly instalments of ₹ 1000 each. * **Calculation:** The principal outstanding each month is: * 1st month: ₹ 19,000 * 2nd month: ₹ 18,000 * ... * 19th month: ₹ 1,000 * Total principal for 1 month = Sum of an AP = $19000 + 18000 + ... + 1000$. * Sum = $\frac{19}{2} \times (19000 + 1000) = \frac{19}{2} \times 20000 = 1,90,000$. * Total Interest = $\frac{190000 \times 6 \times 1}{100 \times 12} = 950$. * The last instalment covers the regular ₹ 1000 principal plus the total accumulated interest of ₹ 950. * Last Instalment = $1000 + 950 = 1950$. * Since ₹ 1950 is not in the options, the answer is "None of these". ### Exam Strategy & Shortcut Recognize that the outstanding principal forms an Arithmetic Progression: $1000 \times (19 + 18 + ... + 1)$. The sum of the first $n$ natural numbers is $\frac{n(n+1)}{2}$. For $n=19$, sum is 190. So, equivalent principal = 190,000. Calculate 1 month's interest on this. ### Common Pitfall A common error is assuming the 6% rate applies to the entire original ₹ 20,000 or the initial ₹ 19,000 for the whole duration, rather than calculating it on the progressively decreasing outstanding balance. ### Final Answer Therefore, the correct answer is **None of these**.