A sum of P was borrowed and paid back in three equal yearly instalments, each of ₹30,000. If the rate of interest was 5% compounded annually, then the value of P (approximate) is:
Show answer & explanation
Correct answer: C
Explanation
The Correct answer is Option 3 i.e.₹81,697.
Formulae for each installment in case of compound interest
P = x/(1 + r/100) + x/(1 + r/100)2 +..... + x/(1 + r/100)n
x = each installment
Now, according to the question
⇒ P = 30000/(1 + 5/100) + 30000/(1 + 5/100)2 + 30000/(1 + 5/100)3
⇒ P = 30000/(21/20) + 30000/(21/20)2 + 30000/(21/20)3
⇒ P = 30000 × 20/21 + 30000 × 20/21 × 20/21 + 30000 × 20/21 × 20/21 × 20/21
⇒ P = 28571.42 + 27210.88 + 25915.12
⇒ P = 81697.42 or
⇒ P = Rs.81697