math55 HW3 solns (partial)

4C p257 1,3,5, 15,31,33

Solutions to HW#3 math 51(31) WD Smith  (HALF ONLY, WILL DO REST LATER)

1. Borrow $40000, APR 7% pay $310 per month for 20 yrs.

a. Principal = 40000
   Interest = 0.07 annually  
   12 payments per yr
   20 year loan term
   pay amount 310/month.

b. 20*12 = 240 payments total.
  pay 240*310 =   74400 total.

c.  40000 to principal, rest (34400) to interest.

3.a. Y=20 year loan of P=$25000 
   i = APR = 10% = 0.10 
   N=12 (monthly payments & compdg)
   Use loan payment formula
             i/N
PMT = P ---------------
                   -NY
        1 - (1+i/N)
get
                .10/12
PMT = 20000 -------------------- = $241.26.
                          -12*20
            1 - (1+.10/12)
as per month payment.

b. 241.26 * 12 * 20 = $57902.40 total payments over all 20 years.

c. Of that, $25000 pays off the principal and remaining
57902.40-25000 = $32902.40 is interest.

5a. Y=30 year mortgage, P=$150000 principal,
i=.075=7.5%, N=12 (monthly payments & compdg)
so same formula with these numbers
                .075/12
PMT = 150000 -------------------- = $1048.82.
                          -12*30
            1 - (1+.075/12)


b. 1048.82 * 12 * 30 = total payments over all 30 years 
                     = $377575.20.

c. Of that, $150000 pays off the principal and remaining
377575.20-150000 = $227575.20 is interest.


15. Y=3-year loan of P=$10000 at APR=i=0.07=7% requires monthly
payments of 

                .07/12
 PMT = 10000 -------------------- = $308.77.
                          -12*3
            1 - (1+.07/12)

But that is more than you can afford (problem says can afford $220/month).
Meanwhile instead borrowing P=$10000 at APR=i=0.075=7.5% 
for Y=4 years requires monthly payments of 

                .075/12
 PMT = 10000 -------------------- = $241.79
                          -12*4
            1 - (1+.075/12)

still unaffordable.  The final option: Y=5-years at APR=8%

                .08/12
 PMT = 10000 -------------------- = $202.76
                          -12*5
            1 - (1+.08/12)
is affordable.  Interestingly, the solution given in the 
"instructor's guide and solutions manual" was wrong. Good thing I
checked it.

31. Options for buying home (P=$80000 loan):
option 1: 30-year fixed rate 7.25% APR,  closing costs $1200, 1 point.
Monthly payments

                .0725/12
 PMT = 80000 -------------------- = $545.74
                           -12*30
            1 - (1+.0725/12)

1 point means 1% of 80000, that is $800.
So total costs are   545.74*12*30  +  1200       +   800   = $198466.40
                      payments       close costs    1point

option 2: 30-year fixed rate 6.75% APR,  closing costs $1200, 3
points.

                .0675/12
 PMT = 80000 -------------------- = $518.88
                           -12*30
            1 - (1+.0675/12)

3 points means 3% of 80000, that is $2400
So total costs are   518.88*12*30  +  1200       +   2400   = $190396.80
                      payments       close costs    3points
The first option wins as far as total costs are concerned.
Lower interest rate wins for you, despite higher initial "points."

33.a. 20-year loan of $25000 at APR=9%=i=0.09 requires monthly payments

                .09/12
 PMT = 25000 -------------------- = $224.93.
                           -12*20
            1 - (1+.09/12)

b. If pay off loan in only Y=10 not Y=20 years,

                .09/12
 PMT = 25000 -------------------- = $316.69.
                           -12*10
            1 - (1+.09/12)

c. Total payments (20 year plan) = 224.93*20*12 = $53983.20
   Total payments (10 year plan) = 316.69*10*12 = $38002.80.

----