Question 1119946: Younus Limited (YL) has borrowed an amount of Rs. 100,000 at an interest of 10% per annum compounded semi-annually. To pay off the loan at the end of four years, YL has created a sinking fund, which yields a return of 8% per annum compounded quarterly. Determine the amount which YL must deposit at the end of each quarter, in the sinking fund, to settle the loan at the end of four years?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the loan if 100,000 at an interest rate of 10% per year compounded semi-annually.
the loan is to be paid off in 4 years.
to pay off the loan, a sinking fund is set up that yields a return of 8% per year compounded quarterly.
determine the amount that must be deposited at the end of each quarter to settle the loan at the end of 4 years.
the future value of the loan is 147,745.54.
the sinking fund is established with a payment of 10,881.48 at the end of each quarter for 4 years.
at the end of the 4 years, the sinking fund will have 147,745.54 in it.
that is just enough to pay off the loan.
i used an online financial calculator at https://arachnoid.com/finance/ to solve this problem.
here are the results of those calculations.
i also did a cash flow analysis in excel to show the process in which the amount of the loan was calculated and the process in which the payments were used to pay off the loan when it was due.
two accounts were set up.
the first account was the money that was borrowed and the future value of that money at 10% per year compounded semi-annually.
the second account was the payments in the sinking fund that were made at the end of each quarter at 8% per year compounded quarterly to satisfy the future value of the loan that needed to be paid when it was due.
you can see that the money owed on the loan at the end of 4 years
in the first use of the calculator, my inputs were:
present value is equal to 100,000.
interest rate per semi-annual period is 10% / 2 = 5%.
number of semi-annual periods is 4 * 2 = 8.
payment per time period was set to 0.
i then had the calculator tell me what the future value was.
in the second use of the calculator, my inputs were:
present value is equal to 0
future value is equal to $147,745.54
interest rate per quarter is equal to 8$ / 4 = 2%.
number of quarters is equal to 4 * 4 = 16.
payment is made at the end of each time period.
i then had the calculator tell me what the quarterly payments needed to be.
at the end of the fourth year, he owes the bank $147,745.54 and he has exactly that amount in his sinking fund account.
any questions, send me an email.
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