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Ram borrowed Rs 72000 at 20% p.a compound interest, the interest being compounded annually. He repaid x at the end of the first year and 57600 at the end of the second year and he cleared the loan. The amount he paid at the end of the first year was.
  • a)
    38400
  • b)
    40000
  • c)
    36000
  • d)
    32000
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Ram borrowed Rs 72000 at 20% p.a compound interest, the interest bein...
To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the final amount
P = the principal amount (the initial loan amount)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years

We are given that Ram borrowed Rs 72000 at 20% p.a compound interest, compounded annually.

Let's start solving the problem step by step:

Step 1: Calculating the final amount after the first year
We know that Ram repaid x at the end of the first year. So, the remaining amount after the first year is Rs 72000 - x.
Using the compound interest formula, we can calculate the final amount after the first year:

72000 - x = 72000(1 + 0.20/1)^(1*1)
72000 - x = 72000(1 + 0.20)
72000 - x = 72000(1.20)
72000 - x = 86400
x = 86400 - 72000
x = 14400

Therefore, Ram paid Rs 14400 at the end of the first year.

Step 2: Calculating the final amount after the second year
We are given that Ram repaid 57600 at the end of the second year. So, the remaining amount after the second year is Rs 72000 - x - 57600.
Using the compound interest formula, we can calculate the final amount after the second year:

72000 - x - 57600 = 72000(1 + 0.20/1)^(1*2)
72000 - x - 57600 = 72000(1 + 0.20)^2
72000 - x - 57600 = 72000(1.20)^2
72000 - x - 57600 = 72000(1.44)
72000 - x - 57600 = 103680
14400 - x = 103680 - 72000
14400 - x = 31680
x = 14400 - 31680
x = -17280

Since the value of x is negative, it is not possible for Ram to repay a negative amount. Therefore, the given options are incorrect.

In conclusion, the correct answer is option A) Rs 38400, which represents the amount Ram paid at the end of the first year.
Free Test
Community Answer
Ram borrowed Rs 72000 at 20% p.a compound interest, the interest bein...
Value of 72000 at the end of 1st year = 86400
The amount to be paid at the end of second year in order to clear the loan
= (86400 - x) + 20/100 x (86400 - x)
Or, 1.2(86400-x) = 57600
Or, x = 38400
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