Final answer:
The monthly payment for a $300,000 loan with 6% interest and a 30-year term is $1,798.65. Making larger monthly payments by a fraction of 12 ($1,948.54) can help pay off the loan faster. The time and money saved can be calculated by subtracting the number of months saved from the original loan term and multiplying the monthly savings by the number of months saved, respectively.
Step-by-step explanation:
Loan Calculation
To calculate the monthly payments, we will use the formula: PV = R * (1 - (1+i)^(-n)) / i
Where:
PV = Present Value or loan amount
R = Monthly payment
i = Interest rate per period
n = Total number of periods
Using the given loan amount of $300,000, interest rate of 6% (convertible monthly), and a loan term of 30 years:
PV = 300,000
i = 0.06/12 = 0.005
n = 30*12 = 360
Substituting these values into the formula:
300,000 = R * (1 - (1+0.005)^(-360)) / 0.005
Solving for R:
R = 300,000 * 0.005 / (1 - (1+0.005)^(-360))
Using a calculator, the monthly payment (R) comes out to be $1,798.65.
Making Larger Monthly Payments
If the monthly payments were larger by a fraction of 12 (equivalent to making 13 payments a year instead of 12), we need to calculate the monthly payment (R') for the same loan amount:
R' = 300,000 * 0.005 / (1 - (1+0.005)^(-360/12))
Using a calculator, the monthly payment (R') comes out to be $1,948.54.
By making larger monthly payments, the loan can be paid off faster. The time saved can be calculated by subtracting the number of months it takes to pay off the loan with larger payments (294.5 months) from the original loan term (360 months). The amount of money saved can be calculated by multiplying the monthly savings ($1,798.65 - $1,948.54) by the number of months saved.