Question

You plan to purchase a $360,000 house using either a 30-year mortgage obtained from your local savings bank with a rate of 8.60 percent, or a 20-year mortgage with a rate of 7.50 percent. You will make a down payment of 15 percent of the purchase price. a. Calculate the amount of interest and, separately, principal paid on each mortgage. What is the difference in interest paid? b. Calculate your monthly payments on the two mortgages. What is the difference in the monthly payment on the two mortgages? For all requirements, do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16)) Interest under 20-year mortgage Interest under 30-year mortgage Difference in interest paid a. b. Monthly payment under 20-year mortgage Monthly payment under 30-year mortgage Difference in monthly payment

Answer 1

a

Interest - 20yr mortgage		285,627.64
Interest - 30yr mortgage		548,854.50
Difference in interest		263,226.86

Monthly payment	=	[P * R * (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	306,000.00
Rate of interest per period:
Annual rate of interest		7.500%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.075 /12 =	0.6250%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	20
Total number of payments	N	20*12 =	240
Period payment using the formula	=	[ 306000*0.00625*(1+0.00625)^240] / [(1+0.00625 ^240 -1]
Monthly payment	=	2,465.12
Total interest pay:
Total payments	=	2465.12*240
		591,627.64
Less principle amount		306,000.00
Interest payment- Finance charge		285,627.64

30 yr mortgage workings:

Monthly payment	=	[P * R * (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	306,000.00
Rate of interest per period:
Annual rate of interest		8.600%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.086 /12 =	0.7167%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	30
Total number of payments	N	30*12 =	360
Period payment using the formula	=	[ 306000*0.00717*(1+0.00717)^360] / [(1+0.00717 ^360 -1]
Monthly payment	=	2,374.60
Total interest pay:
Total payments	=	2374.6*360
		854,854.50
Less principle amount		306,000.00
Interest payment- Finance charge		548,854.50

b

Monthly payment - 20 yr		2,465.12
Monthly payment - 30 yr		2,374.60
Difference in interest		90.52