Question
Download Solution PDFIf a sum of ₹1,00,000 is to be paid back in two equal annual instalments at 2\(\frac 3 4\) percent compound interest per annum in case of annual compounding, then what is the value of each installment? (Rounded off to nearest integral value)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Principal sum = ₹1,00,000
Rate of interest = 2.75%
Compound interest and annual compounding.
Concept:
For repayment in two equal annual instalments, each instalment consists of principal as well as interest. For the first instalment, the interest is calculated
for one year, while of the second instalment, it is calculated for two years.
Calculation:
Let P be the value of each instalment.
⇒ According to the concept, we have:
⇒ 100000 = P/(1 + 0.0275) + P/(1 + 0.0275)2
⇒ 100000 = P/(1.0275) + P/(1.0275)2
⇒ 2.0275P = 100000 × (1.0275)2
⇒ P = 100000 × (1.0275)2/2.0275
⇒ P = Rs. 52072
Therefore, the value of each installment is Rs. 52,072.
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