Multiple choice

What annual payment will discharge a debt of Rs. $7620$ due in $3$ years at $16\displaystyle \frac{2}{3}\%$ per annum compound interest?

  1. Rs. $2540$
  2. Rs. $3430$
  3. Rs. $3260$
  4. Rs. $3380$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Rate = 50/3%. Annual payment P satisfies P/(1+r) + P/(1+r)^2 + P/(1+r)^3 = 7620. Solving this for P gives 3430.

AI explanation

Using the formula for the present value of equal annual payments P = x/(1 + r/100) + x/(1 + r/100)^2 + x/(1 + r/100)^3, the rate of 16 2/3 per cent is 1/6, so 1 + r/100 equals 7/6. The equation becomes 7620 = x/(7/6) + x/(7/6)^2 + x/(7/6)^3, which simplifies to 7620 = 6x/7 + 36x/49 + 216x/343. Finding a common denominator of 343 gives 7620 = 294x/343 + 252x/343 + 216x/343 = 762x/343, so x = 7620 * 343 / 762, making the annual payment 3430.

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