Question

kurtis is expecting a promotion which, hopefully, comes with a raise. he would like his raise to help him correct a high debt-to-income (dti) ratio of 43%. his current annual salary is $53,000. how much of a raise would kurtis need applied to his annual salary to get his dti ratio down to a more reasonable 36%?
a. $4,437
b. $8,627
c. $10,305
d. $63,305
please select the best answer from the choices provided
a
b
c
d

Explanation:

Step1: Find current debt

First, we know that Debt - to - Income (DTI) ratio is calculated as $\text{DTI}=\frac{\text{Debt}}{\text{Income}}$. Given the current income $I_1 = \$53,000$ and current DTI ratio $r_1=43\% = 0.43$. So, the current debt $D$ can be found by rearranging the formula: $D = r_1\times I_1$.
$D=0.43\times53000 = 22790$

Step2: Let the new income be $I_2$

We want the new DTI ratio $r_2 = 36\%=0.36$ and the debt $D$ remains the same (since we are only changing the income via a raise). Using the DTI formula again: $r_2=\frac{D}{I_2}$, we can solve for $I_2$: $I_2=\frac{D}{r_2}$.
Substitute $D = 22790$ and $r_2 = 0.36$ into the formula: $I_2=\frac{22790}{0.36}\approx63305.56$

Step3: Calculate the raise amount

The raise amount $R$ is the difference between the new income and the old income: $R=I_2 - I_1$.
$R = 63305.56-53000=10305.56\approx10305$ (closest to option c: $\$10,305$)

Answer:

c. $10,305$