Question

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

Answer 1

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.