Final answer:
Divya will end up paying approximately $167,805.60 in total interest on her loan of $248,000.
Step-by-step explanation:
To find the total interest paid, we can use the formula:
Total Interest = Total Loan Cost - Principal Amount
First, let's calculate the total loan cost:
Convert the annual interest rate to a decimal: 3.8% = 0.038
Calculate the monthly interest rate: 0.038 ÷ 12 = 0.003167
Calculate the total number of months (30 years × 12 months/year = 360 months)
Use the formula for the monthly payment of a mortgage:
Monthly Payment = Loan Amount × (Monthly Interest Rate ÷ (1 - (1 + Monthly Interest Rate)^(-Total Number of Months)))
Loan Amount = $248,000
Monthly Interest Rate = 0.003167
Total Number of Months = 360
Substituting the values into the formula, we get:
Monthly Payment = $248,000 × (0.003167 ÷ (1 - (1 + 0.003167)^(-360)))
Monthly Payment ≈ $1,155.01
Next, calculate the total loan cost:
Total Loan Cost = Monthly Payment × Total Number of Months
Total Loan Cost = $1,155.01 × 360
Total Loan Cost ≈ $415,805.60
Finally, subtract the principal amount from the total loan cost to find the total interest paid:
Total Interest = Total Loan Cost - Principal Amount
Total Interest = $415,805.60 - $248,000
Total Interest ≈ $167,805.60