To calculate the first monthly payment that includes more toward principal than interest, we can use an amortization schedule for each interest rate.
For a 4.0% rate:
Loan amount: $120,000
Loan term: 30 years
Monthly interest rate: (4.0% / 100) / 12 = 0.0033333
Monthly payment: P
Principal paid: PP
Interest paid: IP
Remaining loan balance: RB
Amortization schedule:
| Month | P | PP | IP | RB |
|-----------|-------|--------|--------|--------|
| 1 | P | ? | IP | RB |
| 2 | P | ? | IP | RB |
| ... | ... | ... | ... | ... |
| N-1 | P | ? | IP | RB |
| N | P | ? | IP | RB |
To find the first monthly payment with more toward principal than interest, we need to find the month where PP becomes greater than IP.
For a 12.5% rate:
Loan amount: $120,000
Loan term: 30 years
Monthly interest rate: (12.5% / 100) / 12 = 0.0104167
Monthly payment: P
Principal paid: PP
Interest paid: IP
Remaining loan balance: RB
Amortization schedule:
| Month | P | PP | IP | RB |
|-----------|-------|--------|--------|--------|
| 1 | P | ? | IP | RB |
| 2 | P | ? | IP | RB |
| ... | ... | ... | ... | ... |
| N-1 | P | ? | IP | RB |
| N | P | ? | IP | RB |
Again, we need to find the month where PP becomes greater than IP.
Unfortunately, the necessary information to complete the tables and calculate the specific months in question is missing from the original question.
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.
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