You may remember seeing home mortgage interest rates fluctuate widely in a period of not too many years. Refer to the following tables, which compare the amortization of a $120,000, 30-year mortgage for rates of 4.0% and 12.5%. Give the first monthly payment that includes more toward principal than toward interest for (a) a 4.0% rate, and (b) a 12.5% rate.
4.0% Interest, Monthly Payment: $572.90
Payment
Number
Interest
Payment
Principal
Payment
Balance of
Principal
Initially
120,000.00
1
400.00
172.90
119,827.10
2
399.42
173.48
119,653.62
3
398.85
174.05
119,479.57
12
393.55
179.35
117,886.76
60
362.49
210.41
108,537.02
152
287.12
285.78
85,851.63
153
286.17
286.73
85,564.90
230
202.43
370.47
60,358.56
231
201.20
371.70
59,986.86
294
114.50
458.40
33,890.53
295
112.97
459.93
33,430.60
296
111.44
461.46
32,969.13
359
3.80
569.10
571.00
360
1.90
571.00
0.00
Totals:
86,243.41
120,000.00
12.5% Interest, Monthly Payment: $1280.71
Payment
Number
Interest
Payment
Principal
Payment
Balance of
Principal
Initially
120,000.00
1
1,250.00
30.71
119,969.29
2
1,249.68
31.03
119,938.26
3
1,249.36
31.35
119,906.91
12
1,246.29
34.42
119,609.63
60
1,224.11
56.60
117,458.11
152
1,133.87
146.84
108,704.57
153
1,32.34
148.37
108,556.20
230
951.19
329.52
90,984.42
231
947.75
332.96
90,651.46
294
641.10
639.61
60,905.68
295
634.43
646.28
60,259.40
296
627.70
653.01
59,606.39
359
26.27
1254.44
1267.51
360
13.20
1267.51
0.00
Totals:
641,055.35
120,000.00
(a) For a 4.0% interest rate, the first monthly payment that includes more toward principal than toward interest is the 360th payment. The payment includes $1.90 toward interest and $571.00 toward principal.
(b) For a 12.5% interest rate, the first monthly payment that includes more toward principal than toward interest is also the 360th payment. The payment includes $13.20 toward interest and $1,267.51 toward principal.
(a) For the 4.0% interest rate, the first monthly payment that includes more toward principal than toward interest is payment number 230.
(b) For the 12.5% interest rate, the first monthly payment that includes more toward principal than toward interest is payment number 295.
To find the first monthly payment that includes more toward principal than toward interest for a given interest rate, you need to look at the amortization tables provided for each interest rate.
For the 4.0% interest rate:
The first monthly payment that includes more toward principal than toward interest occurs on payment number 359. At that point, the interest is only $3.80, while the payment amount is $571.00. This means that $567.20 is going towards principal in that payment.
Therefore, for the 4.0% rate, the first monthly payment that includes more toward principal than toward interest is $571.00.
For the 12.5% interest rate:
The first monthly payment that includes more toward principal than toward interest occurs on payment number 359. At that point, the interest is $26.27, while the payment amount is $1,267.51. This means that $1,241.24 is going towards principal in that payment.
Therefore, for the 12.5% rate, the first monthly payment that includes more toward principal than toward interest is $1,267.51.