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# Calculating annual payment of a mortgage

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Q1: You are thinking of purchasing a house. The house costs \$350,000. You have \$50,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price. The bank is offering a 30-year mortgage that requires annual payments and has an interest rate of 7% per year. What will your annual payment be if you sign up for this mortgage?

Q2: You would like to buy the house, but can only afford to pay \$23,500 per year. The bank agrees to allow you to pay this amount each year, yet still borrow \$300,000. At the end of the mortgage (in 30 years), you must make a balloon payment; that is, you must repay the remaining balance on the mortgage. How much will this balloon payment be?

#### Solution Preview

Q1: You are thinking of purchasing a house. The house costs \$350,000. You have \$50,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price. The bank is offering a 30-year mortgage that requires annual payments and has an interest rate of 7% per year. What will your annual payment be if you sign up for this mortgage?

Loan amount = \$350000-\$50000=\$300,000
Rate of interest = 7% per annum
Period = ...

#### Solution Summary

Solution describes the steps for calculating annual payments for a loan. It also calculate the balloon payment to be made at the end of loan tenure if annual payments made are less than actual amount.

\$2.19

## Compound Interest

Chinn Wong wishes to purchase a \$600,000 house. She has accumulated a \$120,000 down payment, but she wishes to borrow \$480,000 on a 30-year mortgage. For simplicity, assume annual mortgage payments occur at the end of each year and there are no loan fees.

1. What are Wong's annual payments if her interest rate is:
a. 8%
b. 10%
c. 12%
all compounded annually?

2. Repeat number 1 for a 15-year mortgage.

3. Suppose Wong had to choose between a 30-year and a 15-year mortgage, either one at a low 10% interest rate. Compute the total payments and total interest paid on
a. a 30-year mortgage and
b. a 15-year mortgage.

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