Question

Dahlia is trying to decide which bank she should use for a loan she wants to take out. In either case, the principal of the loan will be $19,450, and Dahlia will make monthly payments. Bank P offers a nine-year loan with an interest rate of 5. 8%, compounded monthly, and assesses a service charge of $925. 0. Bank Q offers a ten-year loan with an interest rate of 5. 5%, compounded monthly, and assesses a service charge of $690. 85. Which loan will have the greater total finance charge, and how much greater will it be? Round all dollar values to the nearest cent. A. Loan Q’s finance charge will be $83. 73 greater than Loan P’s. B. Loan Q’s finance charge will be $317. 88 greater than Loan P’s. C. Loan P’s finance charge will be $20. 51 greater than Loan Q’s. D. Loan P’s finance charge will be $234. 15 greater than Loan Q’s.

Answer 1

Answer:

Loan Q’s finance charge will be $83.73 greater than Loan P’s

Step-by-step explanation:

Using EMI Formula

EMI = [P x R x (1+R)^N]/[(1+R)^N-1]

Loan P

P = $19,450

R = 5.8/1200

N = 9 * 12 = 108

EMI = 231.6 $

Amount Paid = 231.6 * 108 = $ 25012.8

Interest Paid = 25012.8 - 19450 = $ 5562.8

Service Charge = $ 925

Total Finance Charges = $ 6487.8

Loan Q

P = $19,450

R = 5.5/1200

N = 10 * 12 = 120

EMI = 211.1 $

Amount Paid = $ 25330.8

Interest Paid = 25330.8 - 19450 = $ 5880.8

Service Charge = $ 690.85

Total Finance Charges = $ 6571.65

Loan Q - Loan P fiance charges = $ 83.85

Loan Q’s finance charge will be $83.73 greater than Loan P’s is closet

Answer 2

Loan Q’s finance charge will be $83.73 greater than Loan P’s.

Given

The principal of the loan will be $19,450, and Dahlia will make monthly payments.

Bank P offers a nine-year loan with an interest rate of 5.8%, compounded monthly, and assesses a service charge of $925.00.

Bank Q offers a ten-year loan with an interest rate of 5.5%, compounded monthly, and assesses a service charge of $690.85.

What is a loan payment?

To solve this, we will use the formula for loan payment:

$\rm P=\dfrac{\frac{x}{n}PV}{1-(1+\dfrac{r}{n})^{-nt}}$

Where P is the payment; PV is the present debt; r is the interest rate; n is the number of payments per year; t is the time.

Working for bank P:

PV = 19450

r = 5.8 or 0.058

t = 9

n = 12

Putting the values in the formula we get:

$\rm P=\dfrac{\frac{x}{n}PV}{1-(1+\dfrac{r}{n})^{-nt}}\\\\P=\dfrac{\frac{0.058}{12}\times 19450}{1-(1+\dfrac{0.058}{12})^{-12 \times 9}}\\\\ P=231.59$

Dahlia's monthly payment is $231.59. So, her total payment for 9 years will be;

$\rm 231.59\times9\times 12=25011.72$

A finance charge will be = total future value minus loan amount plus service charge.

= 25011.72 -19450 +925 = $6486.72

Working for bank Q:

PV = 19450

r = 5.5 or 0.055

t = 10

n = 12

Putting the values in the formula we get:

$\rm P=\dfrac{\frac{x}{n}PV}{1-(1+\dfrac{r}{n})^{-nt}}\\\\P=\dfrac{\frac{0.055}{12}\times 19450}{1-(1+\dfrac{0.055}{12})^{-12 \times 10}}\\\\ P=211.08$

Dahlia's monthly payment is $231.59. So, her total payment for 10 years will be;

$\rm 211.08\times 10\times 12=25329.60$

The finance charge will be = 25329.60  -19450 +690.85 = $6570.45

Therefore,

The difference between both bank's finance charges:

$6486.72-$6570.45 = $83.73

Hence, Loan Q’s finance charge will be $83.73 greater than Loan P’s.

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