If a bar care of for to make a monthly principal and interest payment of $1000 in the lender 18 830 year at 5 1/2% or a 20 year loan at 1/2%, which is the largest lol round to the nearest hundred
To compare the two loan options, let's calculate the monthly principal and interest payments for each loan.
Loan 1: 18-year loan at 5 1/2%
Using the formula for calculating the monthly payment on a loan:
P = principal amount (loan amount)
r = monthly interest rate
n = total number of monthly payments
Principal = $18,830
Monthly interest rate = (5 1/2)% = 0.055
Total number of monthly payments = 18 years * 12 months/year = 216 months
Using the formula:
Monthly Payment = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
P = $18,830
r = 0.055/12 = 0.0045833 (monthly interest rate)
n = 216
Monthly Payment = (18,830 * 0.0045833 * (1 + 0.0045833)^216) / ((1 + 0.0045833)^216 - 1)
Monthly Payment ≈ $135.56
Loan 2: 20-year loan at 1/2%
Using the same formula:
Principal = $18,830
Monthly interest rate = (1/2)% = 0.005
Total number of monthly payments = 20 years * 12 months/year = 240 months
Using the formula:
Monthly Payment = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
P = $18,830
r = 0.005/12 = 0.0004167 (monthly interest rate)
n = 240
Monthly Payment = (18,830 * 0.0004167 * (1 + 0.0004167)^240) / ((1 + 0.0004167)^240 - 1)
Monthly Payment ≈ $84.23
Therefore, the second loan option with a 20-year term at 1/2% interest rate has the larger monthly principal and interest payment, totaling approximately $84.23.
To compare the loan options, we need to calculate the monthly payments for both loans.
For the first loan option, with a term of 18 years and an interest rate of 5.5%, we can use the following formula to calculate the monthly payment:
P = (r * A) / (1 - (1 + r)^(-n))
Where:
P = Monthly payment
A = Loan amount
r = Monthly interest rate
n = Total number of payments
For the second loan option, with a term of 20 years and an interest rate of 0.5%, we can use the same formula to calculate the monthly payment.
Now let's calculate the monthly payments for both options:
For the first loan option:
A = $18,830
r = 5.5% per year / 12 months = 0.0045833 (monthly interest rate)
n = 18 years * 12 months = 216 months
P1 = (0.0045833 * $18,830) / (1 - (1 + 0.0045833)^(-216))
P1 ≈ $146.34
For the second loan option:
A = $18,830
r = 0.5% per year / 12 months = 0.0041667 (monthly interest rate)
n = 20 years * 12 months = 240 months
P2 = (0.0041667 * $18,830) / (1 - (1 + 0.0041667)^(-240))
P2 ≈ $88.26
Now, comparing the two monthly payments, we find that $146.34 (from the first loan option) is higher than $88.26 (from the second loan option).
Therefore, the largest loan payment is the first option with a monthly payment of approximately $146.34, rounded to the nearest hundred.