Question

Suppose you take out a 30 year mortgage for $460000
at an annual interest rate of 3.5%.
You plan to sell the house after 10 years.

Question 1

How much do you owe on the house after five years?

Question 2


How much do you owe on the house after ten years?

After five years you have the opportunity to refinance what you owe
at an interest rate of 3.25% for 30 years.

Question 3

How much would you gain per month during the next 60 periods?

Question 4

What is the maximum amount you would pay to refinance?

Answer 1

1

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                          460,000
Rate of interest per period:
Annual rate of interest		3.500%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.035 /12 =	0.2917%
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	=	[ 460000 × 0.00292 × (1+0.00292)^360] / [(1+0.00292 ^360 -1]
Monthly payment	=	$                                                         2,065.61

Loan balance	=	PV * (1+r)^n - P[(1+r)^n-1]/r
Loan amount	PV =	460,000.00
Rate of interest	r=	0.2917%
nth payment	n=	60
Payment	P=	2,065.61
Loan balance	=	460000*(1+0.00292)^60 - 2065.61*[(1+0.00292)^60-1]/0.00292
Loan balance	=	412,606.24

Balance after five years is $412,606.24

2

Loan balance	=	PV * (1+r)^n - P[(1+r)^n-1]/r
Loan amount	PV =	460,000.00
Rate of interest	r=	0.2917%
nth payment	n=	120
Payment	P=	2,065.61
Loan balance	=	460000*(1+0.00292)^120 - 2065.61*[(1+0.00292)^120-1]/0.00292
Loan balance	=	356,162.99

Amount owed after ten years is $356,162.99

3

New loan
Rate	3.25%
Period	360
Loan amount	$      412,606.24
Monthly payment	$           1,795.69
Less: existing payment	$           2,065.61
Gain per month	$              269.92

4

Particulars	Amount	× factor	Present value
Monthly payment balance	$           2,065.61	$205.21	$      423,874.66
Points paid today			$                       -
Total present value			$      423,874.66
Less: loan balance			$      412,606.24
Savings of refinance			$         11,268.42

Maximum payment for refinance is $11,268.42