Question

Chelsea made monthly payments for four years before her $13,440 loan was paid off. The loan had an interest rate of 5.86%, compounded monthly. Chelsea paid $156.60 in service charges. To the nearest tenth, what percentage of the total cost of the loan did her finance charges comprise? Round all dollar values to the nearest cent. a. 13.6% b. 10.9% c. 9.4% d. 11.9%

Answer 1

Answer:

Option A - 13.6%

Step-by-step explanation:

Given : Chelsea made monthly payments for four years before her $13,440 loan was paid off. The loan had an interest rate of 5.86%, compounded monthly.

Chelsea paid $156.60 in service charges.

To find : Percentage of the total cost of the loan did her finance charges comprise?

Solution : First we find the monthly payment

Formula of monthly payment  

Monthly payment, $M=\frac{\text{Amount}}{\text{Discount factor}}$  

Discount factor $D=\frac{1-(1+i)^{-n}}{i}$  

Where, Amount = $13,440

Rate r= 5.86%=0.0586 compounded monthly

$i=\frac{0.0586}{12}=0.00488$  

Time = 4 years  

$n=4\times12=48$  

Now, put all the values we get,  

$D=\frac{1-(1+i)^{-n}}{i}$  

$D=\frac{1-(1+0.00488)^{-48}}{0.00488}$  

$D=\frac{1-(1.00488)^{-48}}{0.00488}$  

$D=\frac{1-0.791}{0.00488}$  

$D=\frac{0.209}{0.00488}$  

$D=42.827$  

Monthly payment, $M=\frac{\text{Amount}}{\text{Discount factor}}$  

$M=\frac{13440}{42.827}$  

$M=314.77$  

Monthly payment is $314.77

For 4 years or 48 months

Payment is $314.77\times48=15108.96$

Total amount = Payment - Amount

Total amount = 15108.96 - 13440

Total amount = 1668.96

Cost of loan is total amount with service charges is

⇒1668.96+156.60 = $1825.56

Total cost of the loan did her finance charges comprise

$\text{Total cost}=\frac{\text{Cost}}{\text{Amount}}$

$\text{Total cost}=\frac{1825.56}{13440}$

$\text{Total cost}=0.1358$

Total cost in percentage $0.1358\times100=13.58\%$

Approximately,Total cost of the loan did her finance charges comprise is 13.6%

Therefore, Option A is correct - 13.6%

Answer 2

The answer is d.11.9