You borrow 150000 to buy a house If your rate is 6 compounde

You borrow $150,000 to buy a house. If your rate is 6% compounded monthly, determine the following: (a) If you make no payments for five years how much will you owe the bank. (b) How long will it take for your total indebtedness to double. (c) How much will you pay total, if you pay it off all at once after 30 years making no payments in between?

Solution

Amount = Principal( 1 +i)^n

i = 0.06/12 =0.005

for 5 years n = 5*12 = 60

Principal = $ 150,000

Amount = 150,000( 1+ 0.005)^n

= 150,000(1.005)^60 = $ 202327.52 we owe to the bank

b) Total time for total indebtedness to double.

2P = P(1.005)^n

2 = 1.005^n

take log on both sides: ln2 = n*ln(1.005)

n = 138.9 months

No. of years = 138.9/12 =11.6 years

c) After 30 years : Amount = 150,000( 1.005)^30*12 = $ 903386.28