Present Value of an Annuity Carrie and Miranda earn the same salary. However, Mi
ID: 2757620 • Letter: P
Question
Present Value of an Annuity
Carrie and Miranda earn the same salary. However, Miranda has been far more financially responsible. She pays her bills on time and pays off her credit card debt quickly. Carrie had been less financially responsible. She often buys too many shoes and has allowed her credit card balance to balloon. If she is short on cash for a month, she simply decides to not even pay the minimum balance due on her credit card. Now they both are looking to buy apartments. Miranda decides she can afford to make $3,500 payments, but Carrie can only make $1,500 payments and pay off her credit card debt, too. Miranda qualifies for a 6%, 30-year mortgage, but because of her bad credit rating Carrie will be charged 7.5 percent on a 30 year mortage. Both will put 20 percent down. How is Carrier's bad credit going to impact her apartment search?
Explanation / Answer
To answer this, we need to calculate that how much amount can both get as a loan with the payment they can make. This can be calculated using below given formula:
PV = Pmt x ((1-((1+r)-n )) / r) x (1+r)
Maximum Loan, Miranda can avail:
PV = $3,500 x ((1-((1+0.06)-30 )) / 0.06) x (1+0.06) = $51,067.52
Maximum Loan, Carrie can avail:
PV = $1,500 x ((1-((1+0.075)-30 )) / 0.075) x (1+0.075) = $19,044.25
The loan amount equals to 80% of the apartment price as the 20% is the down payment. So, the price of the apartment, they can buyr:
Price of apartment, Miranda can buy with 20% down payment:
$51,067.52 + [($51,067.52/80) x (20)] = $63,834.40
Price of apartment, Carrie can buy with 20% down payment:
$19,044.25 + [($19,044.25/80) x (20)] = $23,805.31