Question

TCO C, D) An investor is offered two loan alternatives. Both require level monthly payments to amortize the loan over 25 years. There are no front-end fees. Loan A's proceeds are $800,000. Interest is at 8 percent. Loan B's proceeds are $900,000. Interest is at 9 percent. Required: What is the incremental rate of interest on the additional funds acquired with loan B?

Answer 1

1)	Installment payment for Loan of $800000 (using formula for loan amortization) = 800000*(0.08/12)*(1+0.08/12)^300/((1+0.08/12)^300-1)) =	$     6,174.53
	Total interest paid = 6174.53*300-800000 =	$   10,52,359
2)	Installment payment for Loan of $900000 (using formula for loan amortization) = 900000*(0.09/12)*(1+0.09/12)^300/((1+0.09/12)^300-1)) =	$     7,552.77
	Total interest paid = 7552.77*300-800000 =	$   14,65,831
3)	Incremental installment = 7552.77-6174.53 =	$     1,378.24
4)	Incremental loan = 900000-800000 =	$     1,00,000
5)	Equating [3] and [4], we have
	100000 = 1378.24*PVIFA(r,300)
	Solving for r
	PVIFA(r,300) = 72.5563
	Using online calculators
	PVIFA for n = 300 and r = 1.4% = 70.3258
	for r = 1.3% = 75.3264
	Interpolating r = 1.3+(75.3264-72.5563)/(75.3264-70.3258) =	1.85
	Incremental annual rate for the additional $100000 = 1.85*12 =	22.25%