+89 A couple save for a deposit and then take out a mortgage to buy a house as follows:
(a) They pay equal monthly amounts into a savings account which pays interest of 3.6% p.a. compounded monthly. What is the monthly amount they must deposit in order to have e50,000 at the end of 10 years?
(b) After ten years they buy a house for e250,000 using the e50,000 saved as a deposit. They take out a mortgage on the balance of e200,000 over 25 years at 4% p.a. compounded monthly. What is the monthly payment on the mortgage?
(
c) How much does the bank earn on the mortgage?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - -> answers
a) Fv = c(1+i)^n - 1/i)
50000 = c(1+ 0.036/12)^120 - 1/ 0.036/12
50000= c(144.1857231)
50000/144.1857231 = c
c= 346.7749714
b) PV = c (1-(1+i)^-n/ i)
200000 = c (1- (1 + 0.04/12)^-300/0.04/12
200000 = c (189.452483)
200000/189.452483 = c
c = 1055.67368
c) 1055.67368 x 300
= 316702.104 - 200000
amount bank earns = 116702.104
