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3 years ago

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Carlos took seven years to pay off his loan by making identical quarterly payments. The loan had a principal of $22,375 and 5.49

% interest, compounded quarterly. Carlos paid a total of $28,821.67. How much did Carlos pay in service charges? Round all dollar values to the nearest cent.

2 answers:

melomori [17]3 years ago

5 0

Answer:

Carlos pay in service charges is $1721.3

Step-by-step explanation:

Given : Carlos took seven years to pay off his loan by making identical quarterly payments.

The loan had a principal of $22,375 and 5.49% interest, compounded quarterly.

Carlos paid a total of $28,821.67.

To find : How much did Carlos pay in service charges?

Solution : First we find the monthly payment of the loan

Formula of monthly payment

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

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

Where, Amount = $22,375

Rate r= 5.49%=0.0549 compounded quarterly

$i=\frac{0.0549}{4}=0.013725$

Time = 7 years

$n=7\times4=28$

Now, put all the values we get,

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

$D=\frac{1-(1+0.013725)^{-28}}{0.013725}$

$D=\frac{1-(1.013725)^{-28}}{0.013725}$

$D=\frac{1-0.68270}{0.013725}$

$D=\frac{0.3172}{0.013725}$

$D=23.1177$

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

$M=\frac{22375}{23.1177}$

$M=967.871$

Now payment he has for for 7 years compounded quarterly i.e, for 28

Payment = 967.871 × 28 = $27100.39

Service charges = Total payment - payment

= $28,821.67 - $27100.39

= $1721.27

Therefore, Carlos pay in service charges is $1721.3

Tju [1.3M]3 years ago

3 0

$1,721.31 is the answer to this question

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Option A: $m \angle E=m \angle F=60^{\circ}$ and $m \angle G=120^{\circ}$ so $\angle G$ is supplementary to both $\angle E$ and $\angle F$ , so EFGH is a parallelogram

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