A man borrows Rs.21630 on compound interest and return it in three equ

1.	A man borrows Rs.21630 on compound interest and return it in three equal year installments. Find the installment charge per year if the rate of 20/3% p.a?1. Rs. 10002. Rs. 9813. Rs. 12004. Rs. 22005. Rs.8192
Answer» Correct Answer - Option 5 : Rs.8192 Given: Principal (P) = 21630, Rate (R) = 20/3%, Installment = 3 Formula used: Instalment = \(\frac{x}{{{{(1 + \frac{R}{{100}})}^n}}}\) Calculation: Let, x be the equal instalment Total number of instalment is 3 Accordingly, \(\frac{x}{{1 + \frac{{20}}{{300}}}} + \frac{x}{{{{(1 + \frac{{20}}{{300}})}^2}}} + \frac{x}{{{{(1 + \frac{{20}}{{300}})}^3}}} = 21630\) ⇒ \(\frac{{15x}}{{16}} + \frac{{225x}}{{256}} + \frac{{3375x}}{{4096}} = 21630\) ⇒ (3840x + 3600x + 3375x) = 4096 × 21630 ⇒ 10815x = 4096 × 21630 ⇒ x = (4096 × 21630)/10815 ∴ Installment is 8192

A man borrows Rs.21630 on compound interest and return it in three equal year installments. Find the installment charge per year if the rate of 20/3% p.a?1. Rs. 10002. Rs. 9813. Rs. 12004. Rs. 22005. Rs.8192

Answer» Correct Answer - Option 5 : Rs.8192

Given:

Principal (P) = 21630,

Rate (R) = 20/3%,

Installment = 3

Formula used:

Instalment = \(\frac{x}{{{{(1 + \frac{R}{{100}})}^n}}}\)

Calculation:

Let, x be the equal instalment

Total number of instalment is 3

Accordingly,

\(\frac{x}{{1 + \frac{{20}}{{300}}}} + \frac{x}{{{{(1 + \frac{{20}}{{300}})}^2}}} + \frac{x}{{{{(1 + \frac{{20}}{{300}})}^3}}} = 21630\)

⇒ \(\frac{{15x}}{{16}} + \frac{{225x}}{{256}} + \frac{{3375x}}{{4096}} = 21630\)

⇒ (3840x + 3600x + 3375x) = 4096 × 21630

⇒ 10815x = 4096 × 21630

⇒ x = (4096 × 21630)/10815

∴ Installment is 8192

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