Question

Ankit borrowed Rs. 6000 from bank and returned Rs. 2000 after 6 years ? After 10 years from starting he returned Rs. 5300 and settle his account. What was the rate of interest?
plz answer

Answer 1

Answer:

R = 2.5 % per annum

Step-by-step explanation:

First Assume Simple interest

Money Borrowed = Rs 6000

Money Returned = 2000 + 5300 = Rs 7300

Interest = 7300 - 6000 = Rs 1300

Interest for first 6 Years = 6000 * R * 6/100 = 360R

Interest for next 4 years = 4000 * R * 4/100 = 160R

360R + 160R = 520R

520R = 1300

=> R = 2.5 % per annum

Now consider Compound interest

interest for first 6 Years = 6000 (1 + R/100)⁶ - 6000

Principle amount after 6 years = 6000 (1 + R/100)⁶ - 2000

Interest for next 4 years

= (6000 (1 + R/100)⁶ - 2000) (1 + R/100)⁴  -  (6000 (1 + R/100)⁶ - 2000)

Total interest = Rs 1300

(6000 (1 + R/100)⁶ - 2000) (1 + R/100)⁴  -  (6000 (1 + R/100)⁶ - 2000) + 6000 (1 + R/100)⁶ - 6000 = 1300

=> (6000 (1 + R/100)⁶ - 2000 (1 + R/100)⁴ = 5300

=> 6000(1 + R/100)¹⁰ - 2000(1 + R/100)⁴ = 5300

=> 60(1 + R/100)¹⁰ - 20(1 + R/100)⁴ = 53

looks too complex to solve for r = 2.24 %

Answer 2

Concept: Simple Interest=$\frac{PXRXT}{100}$

Here, P= Principle

R= Rate of interest

T= TIme

Given: Borrowing by Ankit is Rs. 6,000.

Amount returned by the bank after 6 years are Rs. 2,000.

Amount returned by the bank after 10 years are Rs. 5,300.

Find: Calculate the rate of interest.

Solution: Total money returned=Rs. 2,000+5,300

                                                    =Rs. 7,300.

Amount of interest received= Rs.7,300-6,000

                                              = Rs. 1,300.

Simple interest after 6 years=$\frac{6,000XRX6}{100}$

                                               =360R

Simple interest after next 4 years= $\frac{4,000XRX4}{100}$

                                                      =160R

Total interest=360R+160R=1,300

                     = 520R=1,300

                     = R=1300/520

                     = R=2.5%

Final answer: Rate of interest is 2.5%.

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