Question

Calculate the monthly loan payment (MP) given a 6 %, 5 years with monthly compounding.  The loan is for $125,500.

a. Calculate MP (ordinary annuity):

b. Calculate the Loan Balance after 3.5 years:

c. Calculate the MP as an annuity due:

Answer 1

a]	The monthly interest rate = 6%/12 = 0.5% or 0.005 in decimals.
	MP [ordinary annuity-payments made at the month end] = 125500*0.005*1.005^60/(1.005^60-1) =	$           2,426.27
	[Here, the formula for finding PV of an ordinary annuity has been
	adapted.
	PV of ordinary annuity = MP*(1+r)^n-1/((r*(1+r)^n)
	where MP = monthly payment, r = monthly interest rate [0.5%],
	n = 60.
	So we have, 125500 = MP*(1+0.005^60-1)/(0.005*1.005^60)
	and MP = 125500*0.005*1.005^60/(1.005^60-1)]
b]	Balance of the loan after 3.5 years = PV of the remaining 18 MPs.
	[1.5 years * 12 = 18 months] = 2426.27*(1.005^18-1)/(0.005*1.005^18) =	$         41,665.77
c]	MP under annuity due = 125500*0.005*1.005^60/((1.005^60-1)*1.005) =	$           2,414.20