# Home Equity Loan Problems

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```					Annual Rate     0.05 Length                            30 Payments/year        12 Principle
1               2                    3            4          5             6
Payments (\$1,073.64)     (\$1,073.64)          (\$1,073.64) (\$1,073.64) (\$1,073.64) (\$1,073.64)
Interest   (\$833.33)       (\$832.33)            (\$831.33)    (\$830.32)  (\$829.30)     (\$828.28)
(\$240.31)
Payoff     (\$240.31)       (\$241.31)            (\$242.32)       (\$243.33)      (\$244.34)     (\$245.36)
Cumulative (\$240.31)       (\$481.62)            (\$723.94)       (\$967.26)    (\$1,211.60)   (\$1,456.96)

So, after 1 year (12 payments), you owe:                    \$197,049.27

What are the numbers for the last year of the mortgage?                     Starting payment
349               350              351             352              353        354
Interest      (\$52.26)         (\$48.00)          (\$43.73)        (\$39.44)        (\$35.13)    (\$30.80)
Payoff     (\$1,021.39)     (\$1,025.64)        (\$1,029.92)     (\$1,034.21)    (\$1,038.52) (\$1,042.84)

Lesson: first years of mortgage, payments practically all interest, last years, payments more principle.
Go back to first year. Home prices have gone up.

House was bought with 20% downpayment, so principle (loan amount) was 80% of cost

After first year, equity in house is market value - loan outstanding      Say home prices up
Loan outstanding                  \$197,049
Market value                      \$300,000
Equity                            \$102,951                    downpayment + payoff + rise in prices

Let's take out a home equity loan 'against' the equity. Banks want business. Will loan 50% of equity!!
Call this   principle2          \$51,475 rate2                       0.04

1                2                3               4              5             6
Payments      (\$521.16)        (\$521.16)        (\$521.16)       (\$521.16)      (\$521.16)     (\$521.16)
Interest      (\$171.58)        (\$170.42)        (\$169.25)       (\$168.08)      (\$166.90)     (\$165.72)

Payoff        (\$349.58)        (\$350.74)        (\$351.91)       (\$353.09)      (\$354.26)     (\$355.44)
Cumulative    (\$349.58)        (\$700.32)      (\$1,052.24)     (\$1,405.32)    (\$1,759.58)   (\$2,115.03)

After two years, loans against the house are ??? Use cumprinc to calculate what has been paid.
Original loan
1 year          -\$2,951 This is just to check with other calculation
2 years         -\$6,052                                                 outstanding on first loan

Home equity loan
1 year         -\$4,273                                                      outstanding on 2nd loan
Total debt

Payments total                (\$1,594.81)
Old 'rule of thumb': housing should be only 25% of income. So                \$76,550.70 income to comfortably afford these paym

When should lenders [start to] worry?
200000
7             8             9            10          11          12
(\$1,073.64)   (\$1,073.64)   (\$1,073.64)   (\$1,073.64) (\$1,073.64) (\$1,073.64)
(\$827.26)     (\$826.24)     (\$825.21)     (\$824.17)   (\$823.13)   (\$822.09)

(\$246.38)     (\$247.41)     (\$248.44)     (\$249.47)   (\$250.51)   (\$251.56)
(\$1,703.34)   (\$1,950.75)   (\$2,199.19)   (\$2,448.66) (\$2,699.17) (\$2,950.73)

349
355           356           357           358         359         360
(\$26.45)      (\$22.09)      (\$17.71)      (\$13.31)     (\$8.89)     (\$4.45)
(\$1,047.19)   (\$1,051.55)   (\$1,055.93)   (\$1,060.33) (\$1,064.75) (\$1,069.19)

ore principle.

ovalue            250000

rise                 20%

length2                10

7            8             9            10          11           12
(\$521.16)    (\$521.16)     (\$521.16)     (\$521.16)   (\$521.16)    (\$521.16)
(\$164.53)    (\$163.35)     (\$162.15)     (\$160.96)   (\$159.76)    (\$158.55)

(\$356.63)     (\$357.82)     (\$359.01)     (\$360.21)   (\$361.41)   (\$362.61)
(\$2,471.66)   (\$2,829.47)   (\$3,188.48)   (\$3,548.69) (\$3,910.10) (\$4,272.71)

\$193,948

\$47,203
\$241,150

ncome to comfortably afford these payments.
Primary mortgage
AI                                0.06
Years                               30
Price                          400000
dprate                             0.1
downpayment                     40000
Principal                      360000
5 years
Month                                 1              2           3                       4               5…               60            61
payment                     (\$2,158.38)    (\$2,158.38) (\$2,158.38)             (\$2,158.38)     (\$2,158.38)       (\$2,158.38)   (\$2,158.38)
Pay off                       (\$358.38)      (\$360.17)   (\$361.97)               (\$363.78)       (\$365.60)         (\$481.00)     (\$483.40)
Owed                      \$359,641.62     \$359,281.44 \$358,919.47             \$358,555.69     \$358,190.08
Calculating using different formula
Pay off to date               (\$358.38)      (\$718.56)    (\$1,080.53)           (\$1,444.31)    (\$1,809.92)      (\$25,004.32) (\$25,487.72)

Happy story
Value of house                 400000        400000          400000               400000         400000              500000      500000
Equity                     \$40,358.38    \$40,718.56      \$41,080.53           \$41,444.31     \$41,809.92         \$165,004.32 \$165,487.72
Note: equity arising from downpayment + (slow) pay off of mortgage + value of house going up

Unhappy story
Value of house                400000           400000         370000                370000        370000             300000       300000
Equity                    \$40,358.38       \$40,718.56     \$11,080.53            \$11,444.31    \$11,809.92        (\$34,995.68) (\$34,512.28)

Note: borrower gets 'under water' because house is worth less than what is [still] owed.
Last year
62            63             64 …            348              349           350             351             352
(\$2,158.38)   (\$2,158.38)    (\$2,158.38)       (\$2,158.38)      (\$2,158.38)   (\$2,158.38)     (\$2,158.38)     (\$2,158.38)
(\$485.82)     (\$488.25)      (\$490.69)       (\$2,022.88)      (\$2,032.99)   (\$2,043.16)     (\$2,053.37)     (\$2,063.64)

(\$25,973.54) (\$26,461.79)    (\$26,952.48)     (\$334,921.91) (\$336,954.90) (\$338,998.06)      (\$341,051.43)   (\$343,115.07)

500000      500000           500000
\$165,973.54 \$166,461.79      \$166,952.48

300000       300000          300000
(\$34,026.46) (\$33,538.21)    (\$33,047.52)
353             354             355           356             357             358           359             360
(\$2,158.38)     (\$2,158.38)     (\$2,158.38)   (\$2,158.38)     (\$2,158.38)     (\$2,158.38)   (\$2,158.38)     (\$2,158.38)
(\$2,073.96)     (\$2,084.33)     (\$2,094.75)   (\$2,105.22)     (\$2,115.75)     (\$2,126.33)   (\$2,136.96)     (\$2,147.64)

(\$345,189.02)   (\$347,273.35)   (\$349,368.10) ###########     (\$353,589.07)   (\$355,715.40) (\$357,852.36)   (\$360,000.00)
Exercises in using Excel, including looking up functions
Retirement problem
What will you have for retirement if you start out with \$4000 in savings and add \$2000 each year for 20 years?
Initial nestegg                                 4000
Yearly savings                                  2000
Rate                                             0.04
Years                                              20

Hint: look up FV for future value. You will be asked to make choices. Do both. Be careful on signs.

Purchase Choice
Compare paying \$2500 for a new flat screen TV or 4 payments of \$750 for 4 years.
Price                                       2500
Payments                                     750
Number                                         4
brate                                       10%

Hint: look up PV for present value. You will be asked to choose paying at the start of the year versus paying at the end. Do both
ach year for 20 years?

year versus paying at the end. Do both. Be careful on signs.

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