Question

You found your dream vacation cottage in the mountains and your offer of $78,000 was accepted. You plan to put 20% down and will roll the closing costs of $3,500 into the mortgage. Congratulations, your 15 year mortgage has been approved at an interest rate of 4.125%. (You must use the attached Excel loan amortization schedule).
1. How much are you financing?
2. How much are your monthly mortgage payments?
3. How much will you pay in total interest? If, before you began paying the loan: You decided to round your payment up to the nearest $100. How much additional would you pay?
4. How much interest would paying the additional amount save you over the life of the loan?
5. Does this change the total number of payments to satisfy the loan? If so, by how many? Instead of paying the additional, you decide to pay by-weekly.
6. What are your payments? Rather than paying additional what if: You decided to pay bi-weekly payments.
7. How much less will you pay over the life of the loan?

Answer 1

Answer:

financing 62,400 dollars

Monthly Payment   $ 465.48

Total Interest  21,386.4  

Rounding to nearest $ 100

Additional $  34.52

We save up to 16 payments and $2,136.4 in interest.

By-weekly payment  $232.60

Total Interest saved $ 194.4

Explanation:

78,000 less 20% down-payment: 62,400

Monthly  Payment

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV  $62,400.00

time 180

rate 0.0034375

$62400 \div \frac{1-(1+0.0034375)^{-180} }{0.0034375} = C$

C  $ 465.484

Total Interest

quota times time less principal

$ 465.48 x 180 - 62,400 = 21,386.4

$  500  -  $  465.48  =   $  34.52

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C  $500.00

time n

rate 0.0034375

PV $62,400.0000

$500 \times \frac{1-(1+0.0034375)^{-n} }{0.0034375} = 62400$

$(1+0.0034375)^{-n}= 1-\frac{62400\times0.0034375}{500}$

$(1+0.0034375)^{-n}= 0.571$

We now use logaritmics properties to solve for n

$-n= \frac{log0.571}{log(1+0.0034375)$

-163.2956066

180 - 164 = 16 payments

Total Interst 500 x 163.30 - 62,400 = 19,250

Interest savings 21,386.4 - 19,250 = 2,136.4

If payment are bi-weekly:

then payments will be:

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV  $62,400.00

time 360

rate 0.00171875

$62400 \div \frac{1-(1+0.00171875)^{-360} }{0.00171875} = C$

C  $ 232.598

And total Interest:

232.2 x 360 - 62,400 = 21,192

Difference 21,386.4 - 21,192 = $ 194.4