Question

Today, you borrow $300,000 to buy a condo unit. The mortgage rate is 3.75% compounded semi-annually. The loan is to be repaid in equal monthly payments over 19 years. The first payment is due at the end of the first month. What portion (in dollars) of the third payment will be used to pay down the principal balance?

Question 5 options:

$822

$845

$867

$890

$913

Answer 1

	Effective annual interest rate=	(1+periodic interest rate)^m   -1
rs=	Stated interest rate	3.75%
m	number of compoundings in a year	2
rs/m	period interest rate	1.8750000%
	Effective annual interest rate=	(1+0.01875)^2    -1
	Effective annual interest rate=	3.7852%

APR applicable for monthly compounding is:

	Periodic interest rate=	(1+Effective annual interest rate)^ 1/m -1
r=	effective annual interest rate	3.7852%
m	number of periods	12
	Periodic interest rate=	(1+0.0378515625)^1/12    -1
	Periodic interest rate=	0.3101%
	Nominal rate	3.72103%

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                          300,000
Rate of interest per period:
Annual rate of interest		3.7210%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.0372103 /12 =	0.3101%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	19
Total number of payments	N	19 × 12 =	228
Period payment using the formula	=	[ 300000 × 0.0031 × (1+0.0031)^228] / [(1+0.0031 ^228 -1]
Monthly payment	=	$                                                         1,837.23

Period	Beginning liability	Uniform monthly payment	Interest owed	Principal payment	Total owed at end of month
N	A	C	B= A* 0.003101	D=C-B	E=A-D
1	300,000.00	1,837.23	930.26	906.97	299,093.03
2	299,093.03	1,837.23	927.45	909.79	298,183.24
3	298,183.24	1,837.23	924.62	912.61	297,270.63

Answer is 913.

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