I'm confused with this

Question

Miss Crystal Palace just purchased – you guessed it – a crystal palace for $650,000. She
makes a 25% down payment and finances the balance with a mortgage at an interest rate of
5.6% for 15 years, making monthly payments.
a. What amount will she borrow?
b. Complete the amortization table for the first three payments. Show all work?

Answer 1

Hi Tatiana

 

The purchase price is 650000

 

She make a 25% down payment

650000 (.25) = 162,500

 

a)  Therefore she borrows 

650000 - 162500 = 487,500

 

b)  We first need to determine the monthly payment

We can use the following formula

 

Pmt = P[(i/n)(1+i/n)^nt]/[(1+i/n)^nt-1]

Pmt = monthly payment

P = principle borrowed = 487500

i = interest rate (annual) = 5.6%

n = payment frequency = monthly

t = # years of loan = 15

i/n = .056/12 = .0046666

nt = 12(15) = 180

 

Pmt = 487500[.004666(1.004666)¹⁸⁰/(1.004666¹⁸⁰-1) = 5259.448/1.3118 = 4009.20

 

Now we have to set up the amortization table

 

Amortization table

     

            Beginning     Monthly                        Principal     Ending 

Month   Balance        Payment      Interest       Paid         Balance

1          487500.00    4009.20      2275.00     1734.20   485765.80

2          485765.80    4009.20      2266.91     1742,29   484023.51

3          484023.51    4009.20      2258.78     1750.42   482273.09

 

Beginning balance for months 2 and 3 are the prior month's ending balance

Monthly payment is constant as calculated above

Interest = beginning balance x interest rate / 12 (since payments are monthly)

Principal paid = monthly payment - interest

Ending balance = beginning balance - principal paid