Question

Carly and Ryan have applied for a $70000 mortgage loan at an 8% annual interest rate. The loan is for 30 years and Carly and Ryan will pay it in equal monthly payments that include interest. What is the monthly payment amount?

Answer 1

The monthly payment amount for Carly and Ryan's $70,000 mortgage loan at an 8% annual interest rate over 30 years is approximately $513.15.

Step-by-step explanation:

Carly and Ryan's monthly mortgage payment can be calculated using the formula for a fixed-rate mortgage payment, which is
`P = (Pv \cdot r \cdot (1 + r)^n)/((1 + r)^n - 1)`, where:

- ( P ) is the monthly payment,

- ( Pv ) is the present value of the loan (loan amount),

- ( r ) is the monthly interest rate (annual interest rate divided by 12 months and by 100 to convert to a decimal),

- ( n ) is the total number of payments (loan term in years multiplied by 12 months).

Plugging in the values for Carly and Ryan's loan:

`\[ P = (70000 \cdot (0.08/12) \cdot (1 + 0.08/12)^(30 \cdot 12))/((1 + 0.08/12)^(30 \cdot 12) - 1) \]`

Calculating this gives us the monthly payment amount of approximately $513.15.

Understanding mortgage calculations and loan amortization can empower individuals to make informed financial decisions when entering into long-term financial commitments. Familiarizing oneself with these calculations provides insights into how much of the monthly payment goes towards interest and how much towards the principal, aiding in financial planning.