7. Suppose you bought a new home for $240,000 using a 30-year mortgage with monthly payments...

7. Suppose you bought a new home for $240,000 using a 30-year mortgage with monthly payments of $1,516.96. The annual interest rate of the mortgage is 6.5%. After the first 2 years (24 monthly payments), how much money have you paid in interest and how much in principal?

(a) Interest: $36,407.12; Principal: $5,544.74 (b) Interest: $1,516.96; Principal: $234,455.26 (c) Interest: $30,862.38; Principal $1,516.96 (d) Interest: $30,862.38; Principal: $5,544.74

Expert Solution

(d) Interest: $30,862.38; Principal: $5,544.74

Step-1:Calculation of principal repayment

Principal repayment	=	Loan amount	-	Loan remained after 24 payments
	=	$ 2,40,000.00	-	$ 2,34,454.76
	=	$ 5,545.24

Working:

Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	154.5556638		i	=	6.5%/12	=	0.005417
				n	=	360-24	=	336

Loan remained after 24 payments	=	Monthly payment	*	Present value of annuity of 1
	=	$ 1,516.96	*	154.5556638
	=	$ 2,34,454.76

Step-2:Calculation of interest paid

Total repayment		$ 1,516.96	*	24	=	$ 36,407.04
Total Loan repaid						$ 5,545.24

Total Interest paid						$ 30,861.80

jeff jeffy answered 4 months ago

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