Question

You have just bought a house and have taken out a mortgage (an installment) loan for $500,000. This is a 30-year loan that requires monthly payments and the first payment is due one month from today. The APR for the loan is 24%. You are interested to know how much of your 210^th monthly payment will go toward the repayment of principal? That amount is _______________

Question 10 options:

	$762.65
	$9,586.98
	$625.64
	$9,494.78
	$513.24
	$9,382.38
	$421.04
	$9,245.37

Answer 1

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                          500,000
Rate of interest per period:
Annual rate of interest		24.000%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.24 /12 =	2.0000%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	30.00
Total number of payments	N	30 × 12 =	360
Period payment using the formula	=	[ 500000 × 0.02 × (1+0.02)^360] / [(1+0.02 ^360 -1]
Monthly payment	=	$                                                      10,008.02

Principal paid (nth payment)	=	Payment ÷ (1+R)^(N-n+1)
Payment		10,008.02
Rate of interest	R=	2.0000%
nth payment	n=	210
Total payments	N=	360
Principal paid	=	10008.02/(1+0.02^(360-210+1)
Principal paid	=	503.18

Answer is $513.24 (closest)

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