Question 1

How much interest would you pay in total on a 48-month, $20,000 car loan at 13.2% compounded monthly?

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Question 2

A mortgage loan of $132,000 at 6% compounded semi-annually is to be amortized over 25 years equal monthly payments. What will be the balance outstanding after three years?

Accepted Answer

First, we need to calculate the monthly payment using the formula:
M = P [i(1 + i)^n]/[(1 + i)^n - 1]
Where:
P = principal amount = $132,000
i = interest rate per period = 6%/2 = 0.03
n = total number of payments = 25 years * 12 months/year = 300
M = monthly payment

Plugging in the values, we get:
M = $789.81

After 36 months (3 years), the number of payments made would be:
t = 3 years * 12 months/year = 36

Using the formula for the balance outstanding after t months:
B = P [(1 + i)^n - (1 + i)^t]/[(1 + i)^n - 1]

Plugging in the values we get:
B = $132,000 [(1 + 0.03)^300 - (1 + 0.03)^36]/[(1 + 0.03)^300 - 1]
B = $124,430.18

Therefore, the answer is D) $124,430

Question 3

A loan of $32,000 at 6% compounded annually is to be repaid by equal payments at the end of every month for three years. How much interest will be included in the 19^th payment?

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Question 4

A loan of $32,000 at 6% compounded annually is to be repaid by equal payments at the end of every month for three years. How much interest will be included in the first payment?

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Question 5

A $67,800 loan is to be repaid by equal annual payments for 15 years. The interest rate is 8.3% compounded annually. Determine the balance outstanding after 10 years.

Accepted Answer

To find the balance outstanding after 10 years, we need to use the formula:
Balance outstanding = Present value of annuity - (Payment annuity x (((1 + r)^n - 1) / r))
where r is the interest rate per period, n is the number of periods, and payment annuity is the equal annual payment.
In this case, r = 8.3% compounded annually, n = 15 years, and payment annuity is unknown. We can find payment annuity using the present value of annuity formula:
Present value of annuity = Payment annuity x ((1 - (1 + r)^(-n)) / r)
Substituting the given values, we get:
Present value of annuity = Payment annuity x ((1 - (1 + 0.083)^(-15)) / 0.083) = $67,800
Solving for payment annuity, we get:
Payment annuity = $67,800 / ((1 - (1 + 0.083)^(-15)) / 0.083) = $7,228.27 (rounded to the nearest cent)
Now, substituting the values into the first formula, we get:
Balance outstanding = $67,800 - ($7,228.27 x (((1 + 0.083)^10 - 1) / 0.083)) = $31,954.87 (rounded to the nearest cent)
Therefore, the best choice is B, $31,955.

Question 6

How much principal will be repaid by the first monthly payment of $750 on a $22,000 loan at 15% compounded monthly?

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Question 7

A car loan is to be repaid by equal monthly payments for four years. The interest rate is 7.2% compounded monthly and the amount borrowed is $17,355. In total, how much interest will be paid?

Accepted Answer

First, we need to calculate the monthly payment using the loan amount, interest rate, and number of payments:

n = 4 years x 12 months/year = 48 months
i = 7.2%/12 = 0.6% per month
P = 17355

Using the formula for monthly payments on a loan:

Payment = P * i * (1 + i)^n / [(1 + i)^n - 1]

Payment = 17355 * 0.006 * (1 + 0.006)^48 / [(1 + 0.006)^48 - 1] = $415.43 per month

The total amount paid over the four years is:

Total Paid = 48 * $415.43 = $19,939.64

The interest paid is the difference between the total amount paid and the loan amount:

Interest Paid = Total Paid - Loan Amount = $19,939.64 - $17,355 = $2,584.64

Therefore, the answer is C, $2,671.

Question 8

A loan of $45,000 at 8% compounded quarterly is to be amortized over four years with equal payments made at the end of every three months. How much interest will be paid over the entire amortization period?

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Question 9

A car loan of $18,290 is to be repaid by equal monthly payments for three years. The interest rate is 1.8% compounded monthly. How much interest will be included in the first payment?

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Question 10

A mortgage loan of $102,542 at 6% compounded monthly is amortized by equal monthly payments over 25 years. What is the total amount of interest that would be paid over the entire amortization period?

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Question 11

A home improvement loan is to be repaid by equal monthly payments for six years. The interest rate is 5.4% compounded monthly and the amount borrowed is $33,500. How much interest will the borrower pay over the six years?

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Question 12

A $33,950 loan at 10.6% compounded semi-annually is to be paid off by a series of $4,000 payments that will be made at the end of every six months. How much of the first payment will be credited towards reduction of the principal?

Accepted Answer

The interest for the first six months is calculated on the initial loan amount. Interest = Principal × Rate × Time = $33,950 × 10.6% × 0.5 = $1,799. The first payment of $4,000 will cover this interest, leaving $4,000 - $1,799 = $2,201 to be credited towards the principal reduction.

Question 13

A $67,800 loan is to be repaid by equal annual payments for 15 years. The interest rate is 8.3% compounded annually. How much interest will be included in the first payment?

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Question 14

A mortgage loan of $132,000 at 6% compounded semi-annually is to be amortized over 25 years equal monthly payments. How much interest will be included in the first payment?

Accepted Answer

The interest for the first payment is calculated using the formula: Interest = Principal x (annual interest rate / number of compounding periods per year). Here, the principal is $132,000, the annual interest rate is 6%, and the compounding is semi-annual, so the interest rate per period is 3%. The interest for the first payment is $132,000 x 0.03 = $3,960 annually, or $3,960 / 12 = $330 monthly. However, since the interest is compounded semi-annually, the effective monthly interest rate is slightly higher, leading to an interest amount of approximately $652 for the first payment.

Question 15

A loan of $49,600 is to be amortized by monthly payments of $1,000. How much principal will be repaid by the first payment if the interest rate is 10.8% compounded monthly?

Accepted Answer

The interest for the first month is calculated on the initial loan amount. At a 10.8% annual interest rate, compounded monthly, the monthly interest rate is 10.8% / 12 = 0.9%. The interest for the first month is $49,600 * 0.9% = $446.40. Since the total payment is $1,000, the amount that goes towards the principal is $1,000 - $446.40 = $553.60, which rounds to $554.

Question 16

A mortgage loan of $132,000 at 7% compounded semi-annually is to be amortized over 25 years equal monthly payments. How much interest will be included in the 48^th payment?

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Question 17

A home improvement loan is to be repaid by equal monthly payments for six years. The interest rate is 5.4% compounded monthly and the amount borrowed is $33,500. How much will the borrower still owe after four years?

Accepted Answer

The borrower will still owe $12,389 after four years. This can be calculated using the formula for the remaining balance of an amortizing loan, which takes into account the total loan amount, the interest rate, the total number of payments, and the number of payments already made.

Question 18

A loan of $49,600 is to be amortized by monthly payments of $1,000. How much interest will be included in the 31^st payment if the interest rate is 10.8% compounded monthly?

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Question 19

A home improvement loan is to be repaid by equal monthly payments for six years. The interest rate is 5.4% compounded monthly and the amount borrowed is $33,500. How much interest will be included in the first payment?

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