Question

Mortgage Payment:



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:

\[
r = 0.045
\]