Question

Suppose that you decided to buy a new house. The house you want to buy costs $520,000 and the interest rate is 7%. You currently have $130,000 and are required to put a 20% down payment plus an additional 3% of the loan amount as closing costs.

1) When will you have enough money for the down payment and closing costs, assuming that the $80,000 is the only investment that you make?

2) Suppose that you plan to buy the house in five years. How much do you need to save every month to purchase the house?

3) Suppose that the price of the house is the same after three years and that you can get a 30-year mortgage from your bank at an interest of 3.2%. What are the monthly payments on the loan? How much do you have to pay the bank each year?

4) How much do you pay as interest and principal from the first monthly payment?

Answer 1

1.. Down payment= 520000*20%= 104000 &

Closing costs on the loan= (520000-104000)*3%= 12480

totalling--- 104000+12480= $ 116480

Assuming that $80,000 is the only investment that you make

Time taken to have enough money for the above total of down payment and closing costs will be the plug-in value of the following future value equation, ie.

FV=PV*(1+r)^n

ie. 116480=80000*1.07^n

we get the n= 5.55 yrs.

Roughly 6 years

2) If you plan to buy the house in five years, amt. you need to save every month to purchase the house will be

In 5 yrs. --Your savings would have grown to 130000*1.07^5= 182332

Simlarly, down pmt. & closing costs would work out to 116480*1.07^5= 163369

Also, the house price will be 520000*1.07^5= 729327

So, the mortgage amt. will be

729327-(182332-163369)=

710364

With this amt. as the future value of the mortgage, monthly savings Will be

710364=Pmt.(1.005833^60-1)/0.005833

Mthly .savings=710364/((1.005833^60-1)/0.005833)=

9922.37

3. Price of the house being the same after three years ,ie. $ 520000

your savings would have grown to

130000*1.07^3=

159256

so, he can pay the down payment & closing costs on the loan , on his own(out-of his savings)

So,

The amount of the 30-year mortgage loan will be

520000-down pmt.104000=

416000

will be the PV of the mortgage

Now, the

monthly payments on the loan from bank at 3.2% p.a. ,ie.3.2%/12=0.002667 p.m. for 30 yrs. *12 =360 months   will be

Monthly pmt.=PV of mortgage/Annuity factor(for i=0.002667 & n=360)

Mthly. Pmt.=416000/((1-1.002667^-360)/0.002667)=

1799.15

Amount to be paid to the bank each year=

1799.15*360=

647694

4) Amount paid as interest and principal from the first monthly payment

Towards interest-- 416000*0.002667= $ 1109.47    &

Towards principal--- 1799.15-1109.47= $ 689.68