How Long Will It Take to Pay Off a $100,000 Loan with 8% APR?

What is the loan balance when making minimum payments on a $100,000 loan with an 8% APR?

If you make minimum payments on a $100,000 loan with an 8% Annual Percentage Rate (APR), how many months will it take to have a loan balance of $50,000?

Loan Balance When Making Minimum Payments

It will take approximately 131 months (or 10 years and 11 months) to have a loan balance of $50,000 when making minimum payments.

To determine the number of months it will take to have a loan balance of $50,000 when making minimum payments, we need to consider the loan term, the loan amount, and the interest rate.

Given that you purchased a house for $100,000 at an 8% Annual Percentage Rate (APR) and your loan term is 360 months (30 years), we can calculate the minimum monthly payment using the loan details.

To calculate the minimum monthly payment, we can use the amortization formula:

Loan Payment = Loan Amount x (Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

In this case, the Loan Amount is $100,000, and the Monthly Interest Rate is (8% / 12) = 0.00667 (expressed as a decimal).

Let's plug in these values to calculate the minimum monthly payment:

Loan Payment = $100,000 x 0.00667 / (1 - (1 + 0.00667)^(-360))

Loan Payment ≈ $733.76

Now, to determine the number of months it will take to have a loan balance of $50,000, we can calculate the number of remaining payments using the future value of an ordinary annuity formula:

Number of Months = log(Future Value / Loan Payment) / log(1 + Monthly Interest Rate)

Plugging in the values:

Number of Months = log($50,000 / $733.76) / log(1 + 0.00667)

Number of Months ≈ 130.97