Mmm
A couple wishes to borrow $400,000 to buy a house. The bank has off ered them a 30-year loan repayable in 360 equal monthly instalments (at the end of each month) at a nominal interest rate of 5% per annum, compounded monthly.
First I think that you need to work out the monthly payments.
This is a present value of an ordinary annuity problem
PV=400000, i=0.05/12= 1/240 n=360
400000=C∗1−(1+1/240)−3601/240C=400000÷1−(1+1/240)−3601/240
400000((1−(1+1240)(−360))(1240))=2147.2864920485559393
ok so the monthly payment is $2147.29
After 100 monthly payments of the loan, interest rates rise to 6% per annum, compounded monthly. What should the remaining 260 monthy payments be?
Now you need to work out how much is still owing after 100 months worth of payments.
There will still be 260 payments to go at $2147.29 each at 5%pa = 1/240 per month
To do this you need to use the present value of an ordinary annuity formula again.
PV=2147.29∗1−(1+1/240)−2601/240
2147.29×(1−(1+1240)−260)(1240)=340528.5522121297822056
Ok so after 100 months you owe $340528.55
Now you need to use the present value formula again only this time
the interest rate is 6%pa = 0.005 per month
340528.55=C∗1−(1.005)−2600.005C=340528.55÷1−(1.005)−2600.005
340528.55((1−(1.005)−260)0.005)=2343.3529728316450267
So the remaining payments will be $2343.35 per month
+118696 
