Question 1

Solve the problem.
-Sammy borrowed $10,000 to purchase a new car at an annual interest rate of 11%. She is to pay it back in equal monthly payments over a 5-year period. How much total interest will be paid over the period of the loan?
Round to the nearest dollar.
A) $92
B) $3630
C) $1435
D) $3045

Accepted Answer

First, we need to calculate the monthly payment using the formula:

Monthly payment = (P * r * (1 + r)^n) / ((1 + r)^n - 1)

where P is the principal amount (borrowed amount), r is the monthly interest rate (11% / 12 months = 0.0091667), and n is the total number of payments (5 years * 12 months = 60). Plugging in the values, we get:

Monthly payment = (10,000 * 0.0091667 * (1 + 0.0091667)^60) / ((1 + 0.0091667)^60 - 1) = $212.47

Now, we can calculate the total amount paid over the period of the loan by multiplying the monthly payment by the total number of payments:

Total amount paid = Monthly payment * Total number of payments = $212.47 * 60 = $12,748.20

Finally, we can calculate the total interest paid by subtracting the principal amount from the total amount paid:

Total interest paid = Total amount paid - Principal amount = $12,748.20 - $10,000 = $2,748.20

Rounding to the nearest dollar, we get $2,745, which is closest to option D: $3045. First, we need to calculate the monthly payment using the formula for a loan with equal payments:

Monthly Payment = (Loan amount x monthly interest rate) / (1 - (1 + monthly interest rate)^(-total number of payments))

Plugging in the given values, we get:

Monthly Payment = (10,000 x 0.11/12) / (1 - (1 + 0.11/12)^(-5 x 12))

Monthly Payment = $212.47

Next, we need to calculate the total amount paid over the period of the loan, which is simply the monthly payment multiplied by the total number of payments:

Total Payments = Monthly Payment x total number of payments

Total Payments = $212.47 x (5 x 12)

Total Payments = $12,748.20

Finally, we need to calculate the total interest paid, which is the difference between the total payments and the loan amount:

Total Interest = Total Payments - Loan amount

Total Interest = $12,748.20 - $10,000

Total Interest = $2,748.20

Rounding to the nearest dollar gives us $2,745. Therefore, the best choice is D, $3045.

Question 2

Use an amortization table to solve the problem. Round to the nearest cent.
-A $7,000 debt is to be amortized in 15 equal monthly payments of $504.87 at 1.00% interest per month on the
unpaid balance. What is the unpaid balance after the second payment?

Accepted Answer

The answer of Use an amortization table to solve the...

Question 3

Find the present value of the ordinary annuity.
-Payments of $68 made quarterly for 10 years at 8% compounded quarterly
A) $1872.41
B) $1860.17
C) $1829.38
D) $667.63

Accepted Answer

Using the formula for the present value of an ordinary annuity: PV = PMT x ((1 - (1 + r)^(-n)) / r)

PMT = $68 (quarterly)
r = 0.08/4 = 0.02 (quarterly)
n = 10 x 4 = 40 (number of quarterly periods)

PV = 68 x ((1 - (1 + 0.02)^(-40)) / 0.02) = $1,860.17

Therefore, the best choice is B.

Question 4

Use an amortization table to solve the problem. Round to the nearest cent.
-A bank makes a home mortgage loan of $180,000 at 7.25% amortized in equal monthly payments over 30 years.
What is the total amount paid in interest when the mortgage is paid off (round to the nearest dollar)?

Accepted Answer

The answer of Use an amortization table to solve the...

Question 5

Use an amortization table to solve the problem. Round to the nearest cent.
-A $90,000 home was financed by making a 20% down payment and signing a 30-year mortgage at 6.25%
annual interest compounded monthly for the unpaid balance. The first payment is $443.32. How much of the
first month's payment will apply towards reducing the principal?

Accepted Answer

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Question 6

Use an amortization table to solve the problem. Round to the nearest cent.
-You have agreed to pay off a $8,000 loan in 30 monthly payments of $298.79 per month. The interest rate of the
loan is 0.75% per month on the unpaid balance. What is the unpaid balance after 12 monthly payments have
been made?

Accepted Answer

The answer of Use an amortization table to solve the...

Question 7

Find the monthly house payment necessary to amortize the following loan.
-In order to purchase a home, a family borrows $267,000 at 10.8% for 15 yr. What is their monthly payment? Round the answer to the nearest cent.
A) $3394.52
B) $19,108.39
C) $2403.00
D) $3001.27

Accepted Answer

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Question 8

Use an amortization table to solve the problem. Round to the nearest cent.
-The monthly payments on a $76,000 loan at 12% annual interest are $836.76. How much of the first monthly payment will go toward interest?
A) $100.41
B) $736.35
C) $760.00
D) $912.00

Accepted Answer

To calculate the interest portion of the first monthly payment on a loan, you use the annual interest rate and the initial loan balance. The formula to calculate the interest for the first month is: (Annual Interest Rate / 12) * Initial Loan Balance. With an annual interest rate of 12% and an initial loan balance of $76,000, the calculation is: (0.12 / 12) * $76,000 = $760.00. Therefore, $760.00 of the first monthly payment will go toward interest.

Question 9

Use an amortization table to solve the problem. Round to the nearest cent.
-You have purchased a new house and have a mortgage for $90,000 at 6% compounded monthly. The loan is
amortized over 20 years in equal monthly payments of $644.79. Find the total amount paid in interest when the
mortgage is paid off.

Accepted Answer

The answer of Use an amortization table to solve the...

Question 10

Solve the problem. Round to the nearest cent as needed.
-The monthly payments on a $73,000 loan at 13% annual interest are $807.38. How much of the first monthly payment will go toward the principal?
A) $790.83
B) $104.96
C) $702.42
D) $16.55

Accepted Answer

The answer of Solve the problem. Round to the nearest...

Question 11

Find the payment necessary to amortize the loan.
-$12,800; 12% compounded monthly; 48 monthly payments
A) $1542.69
B) $337.31
C) $331.71
D) $337.07

Accepted Answer

The answer of Find the payment necessary to amortize the...

Question 12

Solve the problem. Round to the nearest cent as needed.
-The monthly payments on a $79,000 loan at 14% annual interest are $982.76. How much of the first monthly payment will go toward interest?
A) $921.67
B) $845.17
C) $137.59
D) $1106.00

Accepted Answer

The interest for the first month is calculated on the initial loan amount. At 14% annual interest, the monthly interest rate is 14% / 12 = 1.1667%. The interest for the first month is $79,000 * 1.1667% = $921.67.

Question 13

Find the payment necessary to amortize the loan.
-$2200; 12% compounded quarterly; 8 quarterly payments
A) $282.23
B) $313.64
C) $442.87
D) $313.40

Accepted Answer

First, we need to calculate the quarterly interest rate:
12% divided by 4 quarters = 0.03 or 3%
Next, we need to calculate the total number of periods:
8 quarterly payments = 2 years (8 quarters in 2 years)
Now we can use the formula to find the payment necessary to amortize the loan:
Payment = (Loan amount * quarterly interest rate) / (1 - (1 + quarterly interest rate)^(-total number of periods))
Payment = (2200 * 0.03) / (1 - (1 + 0.03)^(-8)) = $313.40
Therefore, the best choice is D.

Question 14

Find the monthly house payment necessary to amortize the following loan.
-In order to purchase a home, a family borrows $70,000 at 12% for 15 years. What is the monthly payment?
A) $902.99
B) $700.00
C) $46.67
D) $840.12

Accepted Answer

To calculate the monthly payment necessary for this loan, we can use the formula for calculating the monthly payment on an amortized loan:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

Where:
M = monthly payment
P = principal amount (the amount borrowed)
i = interest rate per month (annual rate divided by 12)
n = total number of payments (15 years x 12 months per year = 180 payments)

Plugging in the values for this loan, we get:

M = $70,000 [ 0.01(1 + 0.01)^180 ] / [ (1 + 0.01)^180 – 1]
M = $840.12

Therefore, the monthly house payment necessary to amortize this loan is $840.12, which is answer choice D.

Question 15

Solve the problem. Assume no new purchases are made with the credit card.
-The annual interest rate on a credit card is 20.99%. If a payment of $100.00 is made each month, how long will it take to pay off an unpaid balance of $1546.15?
A) 19 months
B) 18 months
C) 13 months
D) 21 months

Accepted Answer

To find the number of months required to pay off the balance, we can use the formula for the monthly payment on a loan: M = P * (r(1+r)^n) / ((1+r)^n - 1), where M is the monthly payment, P is the principal balance, r is the monthly interest rate, and n is the number of payments. Here, the monthly interest rate is 20.99%/12 = 0.0174917. Solving for n with M = $100 and P = $1546.15 gives approximately 19 months.

Question 16

Use an amortization table to solve the problem. Round to the nearest cent.
-The monthly payments on a $73,000 loan at 13% annual interest are $807.38. How much of the first monthly payment will go toward the principal?
A) $104.96
B) $790.83
C) $16.55
D) $702.42

Accepted Answer

To find the amount going toward the principal, first calculate the interest for the first month: $73,000 * (13% / 12) = $791.04. Subtract this from the monthly payment: $807.38 - $791.04 = $16.34. Rounding to the nearest cent gives $16.55.

Question 17

Use an amortization table to solve the problem. Round to the nearest cent.
-A home was purchased 14 years ago for $70,000. The home was financed by paying a 20% down payment and
signing a 25 year mortgage at 8.5% compounded monthly on the unpaid balance. The market value is now
$100,000. The owner wishes to sell the house. How much equity (to the nearest dollar) does the owner have in
the house after making 168 monthly payments?

Accepted Answer

The answer of Use an amortization table to solve the...

Question 18

Solve the problem. Round to the nearest cent as needed.
-You have decided to buy a new stereo system for $2,500 and agreed to pay in 30 equal quarterly payments at
1.25% interest per quarter on the unpaid balance. How much are your payments?

Accepted Answer

The answer of Solve the problem. Round to the nearest...

Quiz 3: Additional Derivative Topics

Solve the problem. -Sammy borrowed $10,000 to purchase a new car at an annual interest rate of 11%. She is to pay it back in equal monthly payments over a 5-year period. How much total interest will be paid over the period of the loan? Round to the nearest dollar.

Use an amortization table to solve the problem. Round to the nearest cent. -A $7,000 debt is to be amortized in 15 equal monthly payments of $504.87 at 1.00% interest per month on the unpaid balance. What is the unpaid balance after the second payment?

Find the present value of the ordinary annuity. -Payments of $68 made quarterly for 10 years at 8% compounded quarterly

Use an amortization table to solve the problem. Round to the nearest cent. -A bank makes a home mortgage loan of $180,000 at 7.25% amortized in equal monthly payments over 30 years. What is the total amount paid in interest when the mortgage is paid off (round to the nearest dollar)?

Find the monthly house payment necessary to amortize the following loan. -In order to purchase a home, a family borrows $267,000 at 10.8% for 15 yr. What is their monthly payment? Round the answer to the nearest cent.

Use an amortization table to solve the problem. Round to the nearest cent. -The monthly payments on a $76,000 loan at 12% annual interest are $836.76. How much of the first monthly payment will go toward interest?

Solve the problem. Round to the nearest cent as needed. -The monthly payments on a $73,000 loan at 13% annual interest are $807.38. How much of the first monthly payment will go toward the principal?

Find the payment necessary to amortize the loan. -$12,800; 12% compounded monthly; 48 monthly payments

Solve the problem. Round to the nearest cent as needed. -The monthly payments on a $79,000 loan at 14% annual interest are $982.76. How much of the first monthly payment will go toward interest?

Find the payment necessary to amortize the loan. -$2200; 12% compounded quarterly; 8 quarterly payments

Find the monthly house payment necessary to amortize the following loan. -In order to purchase a home, a family borrows $70,000 at 12% for 15 years. What is the monthly payment?

Solve the problem. Assume no new purchases are made with the credit card. -The annual interest rate on a credit card is 20.99%. If a payment of $100.00 is made each month, how long will it take to pay off an unpaid balance of $1546.15?

Use an amortization table to solve the problem. Round to the nearest cent. -The monthly payments on a $73,000 loan at 13% annual interest are $807.38. How much of the first monthly payment will go toward the principal?

Solve the problem. Round to the nearest cent as needed. -You have decided to buy a new stereo system for $2,500 and agreed to pay in 30 equal quarterly payments at 1.25% interest per quarter on the unpaid balance. How much are your payments?