Question

Your friends suggest that you take a 15-year mortgage, because a 30-year mortgage is too long and you will pay a lot of money on interest. If your bank approves a 15-year, $700,000 loan at a fixed nominal interest rate of 12% (APR), then the difference in the monthly payment of the 15-year mortgage and 30-year mortgage will be   ?(Note: Round the final value of any interest rate used to four decimal places. )

It is likely that you won’t like the prospect of paying more money each month, but if you do take out a 15-year mortgage, you will make far fewer payments and will pay a lot less in interest. How much more total interest will you pay over the life of the loan if you take out a 30-year mortgage instead of a 15-year mortgage?

$1,490,250.96

$1,274,272.56

$1,079,892.00

$1,382,261.76

Answer 1

PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream	$         700,000
PMT = the dollar amount of each annuity payment	P
r = the effective interest rate (also known as the discount rate)	12.68%	((1+12%/12)^12)-1)
i=nominal Interest rate	12.00%
n = the number of periods in which payments will be made	15
PV of annuity=	PMT x (((1-(1 + r) ^- n)) / i)
700000=	PMT x (((1-(1 + 12.68%) ^- 15)) / 12%)
Annual payment=	700000/ (((1-(1 + 12.68%) ^- 15)) / 12%)
Annual payment=	$    100,814.12
PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream	$         700,000
PMT = the dollar amount of each annuity payment	P
r = the effective interest rate (also known as the discount rate)	12.68%	((1+12%/12)^12)-1)
i=nominal Interest rate	12.00%
n = the number of periods in which payments will be made	30
PV of annuity=	PMT x (((1-(1 + r) ^- n)) / i)
700000=	PMT x (((1-(1 + 12.68%) ^- 30)) / 12%)
Annual payment=	700000/ (((1-(1 + 12.68%) ^- 30)) / 12%)
Annual payment=	$      86,403.46
Table	15 year	30 year	Variance
Time in years	15	30
Annual payment	$    100,814.12	$      86,403.46
Total payment	$ 1,512,211.76	$ 2,592,103.76
Principal	$       (700,000)	$       (700,000)
Total interest payment	$    812,211.76	$ 1,892,103.76	$ 1,079,892.00
Hence option 3 is the correct answer.