John is going to make a house purchase and borrow

Question

$
325
,
000
$325,000 and has two options.

John can have a mortgage for
30
30 years an interest rate of
4.5
%
4.5% OR a mortgage for
15
15 years at an interest rate of
4.25
%
4.25%

What is
𝑟
r for the
30
30 loan?

Answer 1

To calculate the monthly interest rate \( r \) for the 30-year loan with an interest rate of 4.5%, you can follow these steps:

1. Convert the annual interest rate to a decimal:
   \[ \text{Annual Interest Rate} = 4.5% = \frac{4.5}{100} = 0.045 \]

2. Calculate the monthly interest rate:
   To find \( r \), divide the annual interest rate by 12 (the number of months in a year):
   \[ r = \frac{0.045}{12} \]

3. Perform the division:
   \[ r = 0.00375 \]

So, the monthly interest rate \( r \) for the 30-year loan is \( 0.00375 \), or 0.375%.