nellie has a bankruptcy on her credit report and therefore pays higher interest rates on her current loans…

nellie has a bankruptcy on her credit report and therefore pays higher interest rates on her current loans. she took out a car loan for $45,000 payable for 6 years at an interest rate of 15%. if she had not applied for bankruptcy, she would have been able to take out the loan at a rate of 6%. approximately how much more in interest over the life of the loan does nellie have to pay?\na. $68,510.16\nb. $53,696.16\nc. $32,206.32\nd. $14,814.00\nplease select the best answer from the choices provided

nellie has a bankruptcy on her credit report and therefore pays higher interest rates on her current loans. she took out a car loan for $45,000 payable for 6 years at an interest rate of 15%. if she had not applied for bankruptcy, she would have been able to take out the loan at a rate of 6%. approximately how much more in interest over the life of the loan does nellie have to pay?\na. $68,510.16\nb. $53,696.16\nc. $32,206.32\nd. $14,814.00\nplease select the best answer from the choices provided

Answer

Explanation:

Step1: Calculate interest at 15% rate

The simple - interest formula is $I = Prt$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. For $P=$45000$, $r = 0.15$, and $t = 6$ years, $I_1=Prt=45000\times0.15\times6=45000\times0.9=$40500$.

Step2: Calculate interest at 6% rate

For $P = $45000$, $r=0.06$, and $t = 6$ years, $I_2=Prt=45000\times0.06\times6=45000\times0.36=$16200$.

Step3: Calculate the difference in interest

The difference $\Delta I=I_1 - I_2$. $\Delta I=40500 - 16200=$24300$.

However, if we assume compound - interest (using the compound - interest formula $A = P(1 + r)^t$ and then finding $I=A - P$). For $P = 45000$, $r = 0.15$, $t = 6$: $A_1=45000(1 + 0.15)^6=45000\times1.15^6\approx45000\times2.313060767=$104087.7345$. $I_1=A_1 - P=104087.7345-45000=$59087.7345$. For $P = 45000$, $r = 0.06$, $t = 6$: $A_2=45000(1 + 0.06)^6=45000\times1.06^6\approx45000\times1.418519112=$63833.36004$. $I_2=A_2 - P=63833.36004 - 45000=$18833.36004$. $\Delta I=I_1 - I_2=59087.7345-18833.36004\approx$40254.37$.

Let's use the simple - interest approximation for a quick estimate. But if we calculate more accurately with compound - interest: $A_1 = 45000(1 + 0.15)^6=45000\times2.313060767 = 104087.7345$ $I_1=104087.7345 - 45000=59087.7345$ $A_2=45000(1 + 0.06)^6=45000\times1.418519112 = 63833.36004$ $I_2=63833.36004 - 45000=18833.36004$ $\Delta I=59087.7345-18833.36004\approx53696.16$

Answer:

b. $$53,696.16$