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?
step by step

Answer 1

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

1. Convert the annual interest rate to a decimal:

   • The annual interest rate is given as \( 4.5% \).
   • To convert it into a decimal, divide by 100: \[ 4.5% = \frac{4.5}{100} = 0.045 \]

2. Calculate the monthly interest rate:

   • Since the interest is compounded monthly, we divide the annual interest rate by 12 (the number of months in a year): \[ r = \frac{0.045}{12} \]

3. Perform the calculation: \[ r \approx \frac{0.045}{12} \approx 0.00375 \]

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

Summary:

• Annual interest rate: \( 4.5% = 0.045 \)
• Monthly interest rate \( r = \frac{0.045}{12} \approx 0.00375 \)