Bethany and Samuel are buying a new house. They have $25,000 saved for a down pa
ID: 3032031 • Letter: B
Question
Bethany and Samuel are buying a new house. They have $25,000 saved for a down payment and know that they can afford a monthly payment of $1,500 or less. They also know that the best interest rate they can get is 5.1% annually and they want to sign a 30-year mortgage.
This equation is used to find the monthly payment, m, given the monthly interest rate, i, the principle, P, and the number of interest periods, n, in months:
A. Using the equation, find the largest possible principle P for their situation. In other words, what is the largest amount of money they can borrow? (Hint: To answer the question, you must rearrange the equation.)
B. Since Bethany and Samuel also have $25,000 for a down payment, what is the highest price of a home they can afford?
ixPx(+i 1 m= + IExplanation / Answer
a) m = $1500 ; i = 0.051/12 = 0.00425 ; n= 30*12 = 360
m = [i*P(1+i)^n]/[(1+i)^n -1]
P= m[(1+i)^n -1]/i(1+i)^n
= 1500[ (1.00425^360 -1]/(1.00425^360)
= $276268.65
b) Highest price of a home they can afford = $276268.65 + $25000
= $ 301268.65
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