Question

Consider a 30-year fixed-rate home loan of $545,500 with an interest rate of 3.25%. What is the total amount of interest paid? (Round your answer to the nearest cent.)?

Answer 1

PV of annuity assuming monthly repayment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream	$                545,500
PMT = the dollar amount of each annuity payment	P
r = the effective interest rate (also known as the discount rate)	3.30%	((1+3.25%/12)^12)-1)
i=nominal Interest rate	3.25%
n = the number of periods in which payments will be made in years	30
545500=	PMT x (((1-(1 + r) ^- n)) / i)
545500=	PMT x (((1-(1 + 3.30%) ^- 30)) / 3.25%)
Annual payment=	545500/ (((1-(1 + 3.30%) ^- 30)) / 3.25%)
Annual payment=	$             28,488.61
Total payment made=	28488.61*30
Total payment made=	$           854,658.17
Loan amount	$           545,500.00
Interest payment=	854658.17-545500
Interest payment=	$           309,158.17