​(Annuity **payments)**  To buy a new​ house, you must borrow 

​$155 comma 000155,000. 

 To do​ this, you take out a 

​$155 comma 000155,000​, 

3535​-year, 

88 

percent mortgage.  Your mortgage​ payments, which are made at the end of each year​ (one payment each​ year), include both principal and 

88 

percent interest on the declining balance.  How large will your annual payments​ be?

Question content area bottom

Part 1

The amount of your annual payment will be 

​$enter your response here. 

 ​(Round to the nearest​ cent.)

To find the amount of the annual payment for a mortgage, we can use the formula for the present value of an ordinary annuity, which is often used in loan and mortgage calculations. The formula is as follows:

\[
P = \dfrac{r \cdot PV}{1 - (1 + r)^{-n}}
\]

Where:
- $P$ is the annual payment (which we are solving for),
- $PV$ is the present value of the loan (the amount borrowed),
- $r$ is the annual interest rate in decimal form,
- $n$ is the number of years (or periods) of the mortgage.

### Given:
- Loan amount ($PV$) = $155,000,
- Interest rate ($r$) = 8% per year = 0.08,
- Mortgage term ($n$) = 35 years.

Now, we can substitute these values into the formula:

\[
P = \dfrac{0.08 \cdot 155,000}{1 - (1 + 0.08)^{-35}}
\]

Let me calculate the payment for you.The annual payment for the mortgage will be approximately **$13,299.51**.

Would you like further details on how this was calculated, or do you have any other questions?

Here are 5 related questions to deepen your understanding:
1. How does the duration of a loan affect the size of the payments?
2. What happens to your mortgage payments if the interest rate increases?
3. How does making additional payments affect the overall loan balance and interest paid?
4. How does the concept of an ordinary annuity differ from an annuity due?
5. What is the total amount of interest paid over the life of this mortgage?

**Tip:** Increasing your down payment reduces the amount you need to borrow, which decreases the size of your monthly or annual mortgage payments.

(Annuity payments) To buy a new house, you must borrow $155,000. To do this, you take out a $155,000, 35-year, 8 percent mortgage. Your mortgage payments, which are made at the end of each year (one payment each year), include both principal and 8 percent interest on the declining balance. How large will your annual payments be?

Understand how to calculate the annual payments for a 35-year mortgage loan of $155,000 at an interest rate of 8%. This guide includes a step-by-step solution using the Present Value of Ordinary Annuity formula. Ideal for college-level finance and mathematics students.

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