Question

You expect to live in a house you are planning to own for 5 years, with a $300K loan. You could get a 3/1 ARM amortized over 15 years at 3.9 %. Suppose the expected interest rate of the ARM for years 4 and 5 is 4.5% and 5.5% respectively. MARR is 10% per year compounded monthly.

What is your Present Cost (PC) of this loan option?

What is the outstanding balance of the loan at the end of 5 years?

Suppose, with the same ownership period and loan amount, you could get a Fixed Rate Mortgage amortized over 15 years at 4.2 %.   

What is your Present Cost (PC) of this loan option?

Answer 1

The answer:

since the MARR is compounded monthly the interest rate for number of periods ;

the annual interest rate is 10% and number of interest periods is 12.Therefore

i =10%/12 =.0.1/12 =.0083

Now the future value of compound interest formula is

F =(1+ i)^{n _P}

^{or  $ 300 K =(1+.0083)60 P}

here n =5 years and interest compunded monthly which is 12 therefore n =12*5 =60

P =$ 300/(1+.0083)⁶⁰

^{=$ 182.69}

^{which is the present cost of loan is $ 182.69}

Since the amortized period is 5 years so the total loan of $300 k which is to be divided by the number of the years the loan is taken ie $ 300/5 =$ 60k

So the oustanding balance at the beginning of the fifth year is $ 60 k and the outstanding balance at the end of the fifth year is $ 0k.

Now since the rate of interest is fixed for the number of years is 15 years ie 4.5%

Now applying the same formula as above:

F =(1+i)^n_P

^{_{where F is the future value}}

^{_{P is the present cost}}

^{_{n = number of years which is interest rate i =4.5% ie .045 and number of years is 15*1 =15}}

^{_{Therefore $ 300 k =(1+.045)15 P}}

^{_{therefore P =$ 300/(1+.045)}15}

^{=$155.01 K}

^{So the present cost of loan is $ 155.01 K}