SOLUTION: A borrower avails a loan from the bank at a rate of interest of 10%, compounded annually. He refunds back 50% of the principal after the end of the first year and at the end of sec
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Question 947558: A borrower avails a loan from the bank at a rate of interest of 10%, compounded annually. He refunds back 50% of the principal after the end of the first year and at the end of second year he clears the balance of the principal as well as the total interest amount of Rs. 1280. What is the principal amount of loan?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the assumption is that the interest rate is being earned on the remaining balance at the end of each year.
he starts with x.
that's the principal.
after 1 year he has earned .10 * x in interest.
he removes x/2 at that time.
what he has left invested is .10 * x + .5 * x which is equal to .6 * x.
the amount of money remaining invested in the account is now .6 * x.
the interest earned on this amount of money at the end of the second year is equal to .1 * .6 * x which is equal to .06 * x.
the total interest earned was .10 * x earned at the end of the first year plus .06 * x earned at the end of the second year.
the total interest earned is therefore equal to .10 + .06 = .16 * x.
since the total interest earned is 1280, then the amount invested has to be 1280 / .16 = 8000.
let's see if that's true.
he starts with 8000.
at the end of the first year he earned 10% on that, so he earned 800 in interest.
he takes away half of the principal, so he removed 4000.
what is left invested is 4000 plus 800 = 4800.
at the end of the second year, he earned 10% on that, so he earned 480 in interest.
his total interest earned is 800 + 480 = 1280.
looks good.
i would say that the initial investment, otherwise known as the principal, was 8000.
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