SOLUTION: How many months will it take to pay off $525 debt, with a monthly $15 at the end of each month, if the interest rate is 18% compounded monthly?

The formula is:



 q = amount of annual payment periods = 12 
 r = interest rate = .18
 B = principal = 525
 m = payment amount = 15
 n = number of payment periods = ?  (what we want to find) 
ln means "the natural logarithm" 

[Note: your book may use different letters for these values]

Substituting those values:



On the calculator, that comes out to 50.0006616 payments

or 50 payments, with just a few cents extra on the last payment.

Now here is what the computer gives by going through all 50
months, month by month, always rounding the interest up to the
next penny whenever there is a fraction of a penny in the interest.
[Lenders always round up to the next penny when figuring the interest
regardless of how small the fraction of a penny is.] 

At the end of month #1 the debt of $525 will be increased
by interest $7.88 to $532.88, then the payment of
$15 will reduce the debt to $517.88

At the end of month #2 the debt of $517.88 will be increased
by interest $7.77 to $525.65, then the payment of
$15 will reduce the debt to $510.65

At the end of month #3 the debt of $510.65 will be increased
by interest $7.66 to $518.31, then the payment of
$15 will reduce the debt to $503.31

At the end of month #4 the debt of $503.31 will be increased
by interest $7.55 to $510.86, then the payment of
$15 will reduce the debt to $495.86

At the end of month #5 the debt of $495.86 will be increased
by interest $7.44 to $503.30, then the payment of
$15 will reduce the debt to $488.30

At the end of month #6 the debt of $488.30 will be increased
by interest $7.33 to $495.63, then the payment of
$15 will reduce the debt to $480.63

At the end of month #7 the debt of $480.63 will be increased
by interest $7.21 to $487.84, then the payment of
$15 will reduce the debt to $472.84

At the end of month #8 the debt of $472.84 will be increased
by interest $7.10 to $479.94, then the payment of
$15 will reduce the debt to $464.94

At the end of month #9 the debt of $464.94 will be increased
by interest $6.98 to $471.92, then the payment of
$15 will reduce the debt to $456.92

At the end of month #10 the debt of $456.92 will be increased
by interest $6.86 to $463.78, then the payment of
$15 will reduce the debt to $448.78

At the end of month #11 the debt of $448.78 will be increased
by interest $6.74 to $455.52, then the payment of
$15 will reduce the debt to $440.52

At the end of month #12 the debt of $440.52 will be increased
by interest $6.61 to $447.13, then the payment of
$15 will reduce the debt to $432.13

At the end of month #13 the debt of $432.13 will be increased
by interest $6.49 to $438.62, then the payment of
$15 will reduce the debt to $423.62

At the end of month #14 the debt of $423.62 will be increased
by interest $6.36 to $429.98, then the payment of
$15 will reduce the debt to $414.98

At the end of month #15 the debt of $414.98 will be increased
by interest $6.23 to $421.21, then the payment of
$15 will reduce the debt to $406.21

At the end of month #16 the debt of $406.21 will be increased
by interest $6.10 to $412.31, then the payment of
$15 will reduce the debt to $397.31

At the end of month #17 the debt of $397.31 will be increased
by interest $5.96 to $403.27, then the payment of
$15 will reduce the debt to $388.27

At the end of month #18 the debt of $388.27 will be increased
by interest $5.83 to $394.10, then the payment of
$15 will reduce the debt to $379.10

At the end of month #19 the debt of $379.10 will be increased
by interest $5.69 to $384.79, then the payment of
$15 will reduce the debt to $369.79

At the end of month #20 the debt of $369.79 will be increased
by interest $5.55 to $375.34, then the payment of
$15 will reduce the debt to $360.34

At the end of month #21 the debt of $360.34 will be increased
by interest $5.41 to $365.75, then the payment of
$15 will reduce the debt to $350.75

At the end of month #22 the debt of $350.75 will be increased
by interest $5.27 to $356.02, then the payment of
$15 will reduce the debt to $341.02

At the end of month #23 the debt of $341.02 will be increased
by interest $5.12 to $346.14, then the payment of
$15 will reduce the debt to $331.14

At the end of month #24 the debt of $331.14 will be increased
by interest $4.97 to $336.11, then the payment of
$15 will reduce the debt to $321.11

At the end of month #25 the debt of $321.11 will be increased
by interest $4.82 to $325.93, then the payment of
$15 will reduce the debt to $310.93

At the end of month #26 the debt of $310.93 will be increased
by interest $4.67 to $315.60, then the payment of
$15 will reduce the debt to $300.60

At the end of month #27 the debt of $300.60 will be increased
by interest $4.51 to $305.11, then the payment of
$15 will reduce the debt to $290.11

At the end of month #28 the debt of $290.11 will be increased
by interest $4.36 to $294.47, then the payment of
$15 will reduce the debt to $279.47

At the end of month #29 the debt of $279.47 will be increased
by interest $4.20 to $283.67, then the payment of
$15 will reduce the debt to $268.67

At the end of month #30 the debt of $268.67 will be increased
by interest $4.04 to $272.71, then the payment of
$15 will reduce the debt to $257.71

At the end of month #31 the debt of $257.71 will be increased
by interest $3.87 to $261.58, then the payment of
$15 will reduce the debt to $246.58

At the end of month #32 the debt of $246.58 will be increased
by interest $3.70 to $250.28, then the payment of
$15 will reduce the debt to $235.28

At the end of month #33 the debt of $235.28 will be increased
by interest $3.53 to $238.81, then the payment of
$15 will reduce the debt to $223.81

At the end of month #34 the debt of $223.81 will be increased
by interest $3.36 to $227.17, then the payment of
$15 will reduce the debt to $212.17

At the end of month #35 the debt of $212.17 will be increased
by interest $3.19 to $215.36, then the payment of
$15 will reduce the debt to $200.36

At the end of month #36 the debt of $200.36 will be increased
by interest $3.01 to $203.37, then the payment of
$15 will reduce the debt to $188.37

At the end of month #37 the debt of $188.37 will be increased
by interest $2.83 to $191.20, then the payment of
$15 will reduce the debt to $176.20

At the end of month #38 the debt of $176.20 will be increased
by interest $2.65 to $178.85, then the payment of
$15 will reduce the debt to $163.85

At the end of month #39 the debt of $163.85 will be increased
by interest $2.46 to $166.31, then the payment of
$15 will reduce the debt to $151.31

At the end of month #40 the debt of $151.31 will be increased
by interest $2.27 to $153.58, then the payment of
$15 will reduce the debt to $138.58

At the end of month #41 the debt of $138.58 will be increased
by interest $2.08 to $140.66, then the payment of
$15 will reduce the debt to $125.66

At the end of month #42 the debt of $125.66 will be increased
by interest $1.89 to $127.55, then the payment of
$15 will reduce the debt to $112.55

At the end of month #43 the debt of $112.55 will be increased
by interest $1.69 to $114.24, then the payment of
$15 will reduce the debt to $99.24

At the end of month #44 the debt of $99.24 will be increased
by interest $1.49 to $100.73, then the payment of
$15 will reduce the debt to $85.73

At the end of month #45 the debt of $85.73 will be increased
by interest $1.29 to $87.02, then the payment of
$15 will reduce the debt to $72.02

At the end of month #46 the debt of $72.02 will be increased
by interest $1.09 to $73.11, then the payment of
$15 will reduce the debt to $58.11

At the end of month #47 the debt of $58.11 will be increased
by interest $0.88 to $58.99, then the payment of
$15 will reduce the debt to $43.99

At the end of month #48 the debt of $43.99 will be increased
by interest $0.66 to $44.65, then the payment of
$15 will reduce the debt to $29.65

At the end of month #49 the debt of $29.65 will be increased
by interest $0.45 to $30.10, then the payment of
$15 will reduce the debt to $15.10

At the end of month #50 the debt of $15.10 will be increased
by interest $0.23 to $15.33, then the payment of
$15 will reduce the debt to $0.33

So his last (50th) payment will be $15.33

Edwin