Mortgage Payment:

Question

The equation below helps us determine the monthly payment for a mortgage.

𝑃
𝑎
𝑦
𝑚
𝑒
𝑛
𝑡
=
𝑃

⋅
(
𝑟
𝑛
)
1
−
(
1
+
𝑟
𝑛
)
−
𝑛
𝑡
Payment=
1−(1+
n
r
​
)
−nt

P ⋅(
n
r
​
)
​


P - principal (the borrowed amount)

n - the number of times the loan is compounded in a year

t - the number of years

r - the interest rate but written as a decimal

Example: A mortgage of $500,000 at 4.1% interest for 30 years would have a monthly payment of $2415.99.

John is going to make a house purchase and borrow
$
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 find the interest rate \( r \) for the 30-year loan, we first need to convert the annual interest rate from a percentage to a decimal.

The interest rate given is:

\[ 4.5% \]

To convert this to a decimal, we divide by 100:

\[ r = \frac{4.5}{100} = 0.045 \]

The interest rate \( r \) for the 30-year loan is therefore:

\[ r = 0.045 \]