Question

susan just got a promotion that increased her annual salary from $52,000 to $68,000. susans monthly expenses included a mortgage payment of $1,500, three minimum credit card payments that total $350, a lease payment of $280, a student loan payment of $250, and a personal loan payment of $325. how did susans debt-to-income ratio change with her promotion?

a. susans debt-to-income ratio decreased by about 2%.
b. susans debt-to-income ratio increased by about 2%.
c. susans debt-to-income ratio decreased by about 15%.
d. susans debt-to-income ratio increased by about 15%.

Explanation:

Calculate total monthly debt payments

To find the debt-to-income (DTI) ratio, we first sum all of Susan's monthly debt and housing obligations:

• Mortgage payment: \$1,500
• Credit card payments: \$350
• Lease payment: \$280
• Student loan payment: \$250
• Personal loan payment: \$325

$$ \text{Total Monthly Debt} = 1500 + 350 + 280 + 250 + 325 = 2705 $$

The total monthly debt is \$2,705.

Calculate initial monthly gross income and DTI

Susan's initial annual salary was \$52,000. We divide this by 12 to find her initial monthly gross income:

$$ \text{Initial Monthly Income} = \frac{52000}{12} \approx 4333.33 $$

Now, we calculate her initial DTI ratio:

$$ \text{Initial DTI} = \frac{2705}{4333.33} \approx 0.6242 \text{ or } 62.42\% $$

Calculate new monthly gross income and DTI

Susan's new annual salary is \$68,000. We divide this by 12 to find her new monthly gross income:

$$ \text{New Monthly Income} = \frac{68000}{12} \approx 5666.67 $$

Now, we calculate her new DTI ratio:

$$ \text{New DTI} = \frac{2705}{5666.67} \approx 0.4774 \text{ or } 47.74\% $$

Determine the change in DTI ratio

We find the difference between the initial DTI ratio and the new DTI ratio:

$$ \text{Change in DTI} = 47.74\% - 62.42\% = -14.68\% $$

This represents a decrease of approximately 15%.

Answer:

• a. Susan's debt-to-income ratio decreased by about 2%.
• b. Susan's debt-to-income ratio increased by about 2%.
• c. Susan's debt-to-income ratio decreased by about 15%. (Correct answer)
• d. Susan's debt-to-income ratio increased by about 15%.