Question

You are getting ready to purchase your first home. You wish to purchase a $400,000 home and the bank requires a 20% deposit. Your father-in-law will provide whatever amount you need after using the governments Homestart scheme and you withdraw your savings from Kiwisaver. Interest rates on a 20-year mortgage with fortnightly payments are 6 percent per annum.

a. What will your fortnightly payment be on a 20 year mortgage?

b. After 5 years of paying off this mortgage, you want to increase your fortnightly payment to $1500. Assuming you have paid $96,000 in interest, when will you have your mortgage paid off?

Answer 1

a. What will your fortnightly payment be on a 20 year mortgage?
Home Purchase Value	$400,000
Deposit @ 20%	$80,000
Loan Amount	$320,000
Period (n) in years	20
Frequency of Payments (t) - fortnightly	24
Total Number of Payments (n x t) - 24 x 20	480
Annual Rate of Interest	6%
Fortnightly rate of Interest (6%/ 24)	0.25%
PVIFA = ( 1 - (1+(r/t) ) ^ -n*t) / (r/t)	$279.34
Fortnightly Payment	$1,145.55
b. After 5 years of paying off this mortgage, you want to increase your fortnightly payment to $1500. Assuming you have paid $96,000 in interest, when will you have your mortgage paid off?
Total Amount Including Interest for 20 Years ($1145.55 * 24 * 20)	$549,864.07
Amount Paid After 5 Years ($1145.55 * 24 * 5)	$137,466.02
Total Amount Remaining (Incl. Interest)	$412,398.05
Now, assuming you have paid $96000 in Interest in first 5 years),
Principal Paid = Total Amount Paid - Interest ($137466.02 - $96000)	$41,466.02
To calculate remaining tenure for fortnightly payments of $1500,
Remaining Loan Amount (excl. Interest) ($320000 - $41466.02)	$278,533.98
Period (n) in years	?
Frequency of Payments (t) - fortnightly	24
Total Number of Payments (n x t) - 24 x 20	?
Annual Rate of Interest	6%
Fortnightly rate of Interest (6%/ 24)	0.25%
PVIFA = ( 1 - (1+(r/t) ) ^ -n*t) / (r/t)
Fortnightly Payment (Loan Amount / PVIFA)	$1,500.00
1500 = 278533.98/( 1 - (1+(0.25%) ) ^ -n*t) / (0.25%)
1500 = [278533.98 * 0.25%]/( 1 - (1+(0.25%) ) ^ -n*t)
( 1 - (1+0.25%) ^ -n*t) = [278533.98 * 0.25%]/1500
( 1 - (1+0.25%) ^ -n*t) = 0.464
1-0.464=1.0025^-n*t
0.536=1.0025^-n*t
Using Trial and Error,
10 Years: 1.0025^-240 = 0.549
15 Years: 1.0025^-360 = 0.407
Difference -0.142 for 120 n*t
For difference from 10 Years i.e. 0.536 - 0.549 = -0.142, n*t would be 10.98 or ~11 additional payments
Hence, we get the value, of n * t as 251 i.e. 240 + 11.
Mortgage will then be paid of in 5 Years (120 payments) + 251 payments = 371 payments = 15 years, 5 months and 1 fortnight.