# Compare Loan Options: 30-Year vs 15-Year Loan

## What are the differences in monthly payments and total loan costs between a 30-year loan at 9% APR and a 15-year loan at 8.5% APR for a $110,000 loan amount?

## Monthly Payment and Total Loan Cost Analysis:

The total loan cost for Option 1 is higher than Option 2 despite having a **lower APR**. The monthly payments for Option 1 and Option 2 are $884.21 and $1,057.93 respectively.

Given the loan amount of $110,000:

Option 1: 30-year loan at an APR of 9%

Option 2: 15-year loan at an APR of 8.5%

Let's calculate the monthly payment for Option 1:

Monthly Payment = Loan amount * (r(1+r)^n / (1+r)^n - 1)

where r = **Rate of interest** / 12 (interest rate per month), n = Total number of payments

For Option 1, r = 9%/12 = 0.0075 and n = 30 years * 12 = 360 months

Plugging in these values, **Monthly Payment** for Option 1 = $884.21 (approx.)

Now, let's calculate the monthly payment for Option 2:

For Option 2, r = 8.5%/12 = 0.007083 and n = 15 years * 12 = 180 months

Plugging in these values, Monthly Payment for Option 2 = $1,057.93 (approx.)

To calculate the total loan cost, we need to multiply the monthly payment by the total number of payments (n).

For Option 1, the total loan cost is $318,315.60.

For Option 2, the total loan cost is $190,427.40.

The total loan cost for Option 1 is higher than Option 2 despite having a lower APR.