Present Value of an Annuity Carrie and Miranda earn the same salary. However, Mi
ID: 2757606 • 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. How is Carrier's bad credit going to impact her apartment search?
Explanation / Answer
Present value of Annuity Immediate
PVA = A [ ( 1+r) n -1 ] / r ( 1+r) n
The present value of the Loan Miranda qualifies for a 6%, 30-year mortgage
PVA = $ 3,500 [ ( 1+ 0.06) 30 -1 ] / 0.06 X ( 1+0.06)30
PVA = $ 48,176.88
The present value of the Loan Carrie qualifies for a 7.50 %, 30-year mortgage
PVA = $ 1500 [ ( 1+0.075)30 -1 ] / 0.075 X ( 1+0.075)30
PVA = $ 17,715.57
Due to the Carrier's bad credit she is eligible for a loan whose present value is $ 17,715.57 and this impacts her search for an apartment as the bank would qualify her for a lesser loan when compared to Miranda who can qualify for a higher loan whose present worth is $ 48,176.88 .