Present Value of an Annuity Sandra and Regina earn the same salary. However, Regina has been far more financially responsible. She pays her bills on time and pays off her credit card debt quickly. Sandra 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. Regina decides she can afford to make $3,500 payments, but Sandra can only make $1,500 payments and pay off her credit card debt, too. Regina qualifies for a 6 percent, 30-year mortgage, but because of her bad credit rating Sandra will be charged 7.5 percent on a 30-year mortgage. Both will put 20 percent down. How is Sandra's bad credit going to impact her apartment search?

Question

Present Value of an Annuity Sandra and Regina earn the same salary. However, Regina has been far more financially responsible. She pays her bills on time and pays off her credit card debt quickly. Sandra 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. Regina decides she can afford to make $3,500 payments, but Sandra can only make $1,500 payments and pay off her credit card debt, too. Regina qualifies for a 6 percent, 30-year mortgage, but because of her bad credit rating Sandra will be charged 7.5 percent on a 30-year mortgage. Both will put 20 percent down. How is Sandra's bad credit going to impact her apartment search?

Answer 1

Sandra's bad credit is going to impact her apartment search in several ways, particularly in terms of her ability to afford the mortgage payments and the interest rate she will be charged.

First, let's calculate the present value of an annuity for both Sandra and Regina. The present value of an annuity is the value of a series of equal payments made at regular intervals, and it represents the amount that is needed today to generate those future payments.

For Regina:
- Monthly payment: $3,500
- Mortgage term: 30 years
- Interest rate: 6%

To calculate the present value of an annuity, we can use the formula:

PV = P * [1 - (1 + r)^(-n)] / r

Where PV is the present value, P is the monthly payment, r is the interest rate per period, and n is the number of periods.

Using this formula, we can calculate Regina's present value of the annuity as follows:

PV_Regina = $3,500 * [1 - (1 + 0.06/12)^(-30*12)] / (0.06/12)
PV_Regina ≈ $500,366.36

For Sandra:
- Monthly payment: $1,500
- Mortgage term: 30 years
- Interest rate: 7.5%

Using the same formula, we can calculate Sandra's present value of the annuity as follows:

PV_Sandra = $1,500 * [1 - (1 + 0.075/12)^(-30*12)] / (0.075/12)
PV_Sandra ≈ $295,206.90

From these calculations, we can see that Sandra's present value is significantly lower compared to Regina's. This means that Sandra can afford less expensive apartments compared to Regina, given her lower affordability.

Additionally, Sandra's bad credit rating will result in a higher interest rate on her mortgage. With a 7.5% interest rate compared to Regina's 6%, Sandra will have higher monthly mortgage payments. This means that Sandra's budget for an apartment will be further constrained by her higher mortgage payments, reducing the amount she can afford to spend on housing.

In summary, Sandra's bad credit rating will impact her apartment search by reducing her affordability and increasing her mortgage payments due to the higher interest rate charged. She will have to look for apartments within her lower affordability range and may have more limited options compared to Regina.