Jean is buying a new apartment. She can afford a mortgage payment of $1110 a month, and a down payment of $19000. She obtained a 16-year loan at 4.85% compounded monthly. What is the most expensive apartment she can buy?

Express your answer rounded to the nearest cent!

Apartment price = $ 

$167,040.49

Step-by-step explanation

Step 1: Find the present value of the monthly payment. The formula is:

P = {(A)[1 - (1 + ^r/_n)^-nt]}/(^r/_n)

where:

P = present value of the periodic payment

A = amount of periodic payment

r = rate of interest

n = number of compounding periods per year

t = number of years

In the problem,

P = ?

A = $1,110

r = 4.85% = 0.0485

n = 12 (monthly)

t = 16 years

Using the formula,

P = {(A)[1 - (1 + ^r/_n)^-nt]}/(^r/_n)

P = {(1110)[1 - (1 + ^0.0485/₁₂)^-(12)(16)]}/(^0.0485/₁₂)

P = $148,040.49

Step 2: Find the cost of the apartment by adding the present value of periodic payment and the down payment amount.

$148,040.49 + $19,000 = $167,040.49