Answer:approximately $396,849.46 after 30 years with continuous compounding.
Explanation:
To calculate the cost of the loan after 30 years with continuous compounding, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the total amount after interest
P = the principal amount (loan amount)
e = Euler's number, approximately 2.71828
r = interest rate per period
t = time in years
Given:
Principal amount (loan amount), P = $175,000
Interest rate, r = 3% = 0.03 (as a decimal)
Time, t = 30 years
Using the formula, we can calculate the total amount (A):
A = $175,000 * e^(0.03 * 30)
Now, let's calculate the cost of the loan after 30 years:
A = $175,000 * 2.71828^(0.03 * 30)
Using a calculator or software, we find:
A ≈ $396,849.46
Therefore, the loan will cost approximately $396,849.46 after 30 years with continuous compounding.