Question

A loan of $100,000 is made today. The borrower will make equal repayments of $918 per month with the first payment being exactly one month from today. The interest being charged on this loan is constant (but unknown).

For the following two scenarios (EXCEL HIGHLY REGARDED), calculate the interest rate being charged on this loan, expressed as a nominal annual rate compounding monthly. Give your answer as a percentage to 2 decimal places.

(a) The loan is fully repaid exactly after 240 monthly repayments, i.e., the loan outstanding immediately after 240 repayments is exactly 0.
(1.5 marks)

(b) The term of the loan is unknown but it is known that the loan outstanding 2 years later equals to $85030.

Please show working out so I can understand

Answer 1

	(a)	The loan is fully repaid exactly after 240 monthly repayments,
		i.e., the loan outstanding immediately after 240 repayments is exactly 0.
	Pv	Loan Amount (Present Value)	$100,000
	Nper	Number of Months of Payment	240
	Pmt	Monthly repayments	$918
	Fv	Amount Outstanding at end of 240 months	$0
	Type	Payment at end of months	0
	RATE	Monthly Interest Rate	0.77357%
		(Using RATE Function of excel)
		Nominal Annual Rate=12*0.77357%=	9.28%
	(b)	The term of the loan is unknown but it is known that the
		loan outstanding 2 years later equals to $85030.
	Pv	Loan Amount (Present Value)	$100,000
	Nper	Number of Months of Payment=2Years*12	24
	Pmt	Monthly repayments	$918
	Fv	Amount Outstanding at end of 24months	$85,030
	Type	Payment at end of months	0
	RATE	Monthly Interest Rate	0.31667%
		(Using RATE Function of excel)
		Nominal Annual Rate=12*0.31667%=	3.80%