Question

Amanda Rice has just arranged to purchase a $500,000 vacation home in the Bahamas with a 20 percent down payment. The mortgage has a 5.6 percent APR compounded monthly and calls for equal monthly payments over the next 30 years. Her first payment will be due one month from now. However, the mortgage has an eight-year balloon payment, meaning that the balance of the loan must be paid off at the end of Year 8. There were no other transaction costs or finance charges.

  

How much will Amanda’s balloon payment be in eight years?

Answer 1

Step 1: Find the amount of mortgage.
Step 2: We have to find the monthly payment.
Step 3: We have to find the balance of loan after 8 years.

Step 1: Amount of mortgage.

Purchase price = $500,000
Down payment = 20%
Therefore, down payment = $500,000 * 12% = $100,000

Mortgage = Purchase price - down payment
= $500,000 - $100,000
= $400,000

Step 2: Monthly payment.

To find the amount of monthly payment we can use the Present Value of Annuity formula:

Where,
PVA = Present Value of Annuity
A = Annuity or Payment
i = rate of interest
n = number of years
a = number of payments per year
na = total number of payments

Substituting the values in the formula, we get:

Therefore, the monthly payment = $2,296.32

Step 3: Balance of loan after 8 years.

Here we need to find the balance of loan after 8 years of payment. That means the number of payments till that time = 8 *12 = 96 payments.

In short we need to find the balance after 96th payment.

For that we can use the balance of loan formula:

Where,
PV = Present value / original balance
A = Annuity / Payment
i = rate of interest
a = number of payments per year
n = number of years
na = total number of payments

Substituting the values in the formula, we get:

Therefore, the balloon payment in 8 years =  $348,114.90