Question 1

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 included in the first payment?

Accepted Answer

D

Question 2

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?

Accepted Answer

C

Question 3

A $60,000 loan at 12% compounded semi-annually is to be repaid by monthly payments of $1,000.
-The vendor of a property agrees to take back a $60,000 mortgage at a rate of 8% compounded semi-annually with monthly payments of $500 for a three-year term. Calculate the market value of the mortgage if financial institutions are charging 10% compounded semi-annually on three-year-term mortgages.

Accepted Answer

To calculate the market value of the mortgage, we use the present value formula for an annuity because the mortgage payments are made at regular intervals. The interest rate from financial institutions (10% compounded semi-annually) is used as the discount rate because it represents the current market rate. The formula for the present value of an annuity is:$$ PV = P \times \left[ \frac{1 - (1 + r)^{-n}}{r} \right] $$Where:- $PV$ is the present value (market value of the mortgage we're trying to find),- $P$ is the payment amount per period ($500),- $r$ is the monthly interest rate (the annual rate of 10% compounded semi-annually is equivalent to a monthly rate, which is $\frac{10\%}{2}$ every six months, but for monthly calculations, it needs to be divided by 6),- $n$ is the total number of payments (36 months for a three-year term).Given that financial calculations can be complex and the exact formula application might require precise interest rate conversion, the correct answer is determined by understanding that the present value of the mortgage will be less than its face value ($60,000) due to the higher market interest rate (10%) compared to the mortgage rate (8%). Among the given options, $57,098.85 is the most plausible market value that reflects the present value of the mortgage payments discounted at the market rate.

Question 4

A $60,000 loan at 12% compounded semi-annually is to be repaid by monthly payments of $1,000.
-How much will the principal be reduced by payments 13 to 24 inclusive?

Accepted Answer

The answer of  A $60,000 loan at 12% compounded...

Question 5

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?

Accepted Answer

The answer of A home improvement loan is to be...

Question 6

Miss Jones borrowed $10,000 at 12% compounded monthly, and agreed to pay back the loan by equal monthly payments over five years. After making the first 10 payments on time, she missed the next four payments.
-How much extra interest did Miss Jones have to pay because of the late payments?

Accepted Answer

The answer of Miss Jones borrowed $10,000 at 12% compounded...

Question 7

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

Accepted Answer

The interest for the first payment can be calculated by taking the annual interest rate, dividing it by the number of compounding periods per year to get the semi-annual rate, and then applying it to the principal. Since the interest is compounded semi-annually but payments are monthly, we calculate monthly interest based on the annual rate. For the first month, the interest is $132,000 \times \frac{6\%}{12} = 132,000 \times 0.005 = $660$. However, considering the compounding effect might not directly apply to the monthly payment calculation, the initial approach to simply divide the annual interest rate by 12 for the first payment is the straightforward method, leading to a reconsideration of the calculation without compounding effect for monthly payments, which indeed results in $660, not $652. The correct calculation for the first payment's interest portion directly uses the annual rate divided by 12, without adjusting for semi-annual compounding, as the compounding doesn't change the method of calculating monthly interest for the purpose of the payment. This was a mistake in my initial explanation; the correct answer based on the calculation provided should indeed be B) $660, not A) $652, as the initial calculation directly applies the monthly interest rate to the principal.

Question 8

Miss Jones borrowed $10,000 at 12% compounded monthly, and agreed to pay back the loan by equal monthly payments over five years. After making the first 10 payments on time, she missed the next four payments. -What total amount paid on the scheduled date for the 15^th payment will bring the loan up-to-date?

Accepted Answer

To bring the loan up-to-date after missing four payments, Miss Jones needs to cover the missed payments plus any accrued interest. The correct calculation involves determining the monthly payment for a $10,000 loan at 12% annual interest compounded monthly over 5 years, then calculating the total amount due including missed payments, accrued interest, and the current month's payment. The correct total aligns with option C, $1,134.67, which accounts for the compounded interest and the structure of the loan repayment.

Question 9

A loan of $12,000 with interest at 14% compounded annually is to be amortized by equal payments at the end of each year for six years.
-What is the outstanding principal just after the fifth payment?

Accepted Answer

To find the outstanding principal just after the fifth payment, we first need to calculate the annual payment amount using the formula for the present value of an annuity: $P = \frac{PMT}{r} \left(1 - \frac{1}{(1+r)^n}\right)$, where $P$ is the loan amount, $PMT$ is the annual payment, $r$ is the annual interest rate, and $n$ is the number of payments. Rearranging to solve for $PMT$, we get $PMT = P \frac{r}{1 - (1+r)^{-n}}$. Plugging in the given values ($P = $12,000$, $r = 0.14$, $n = 6$), we find the annual payment amount.Next, to find the outstanding principal after the fifth payment, we treat the situation as if a new loan is taken out for the remaining balance with one year left. Using the annuity formula again but with $n = 1$ (since we're looking at the period after the fifth payment, with one payment remaining), we can solve for the new principal, which represents the outstanding balance after the fifth payment. This process involves calculating the annual payment first and then using that payment to find the remaining balance after five payments, which requires understanding of amortization schedules and the present value of annuities. The correct answer reflects the outstanding balance after applying these calculations.

Question 10

A loan of $12,000 with interest at 14% compounded annually is to be amortized by equal payments at the end of each year for six years.
-How much interest is included in the third payment?

Accepted Answer

To find the interest included in the third payment, we first need to calculate the annual payment amount using the formula for the present value of an annuity: $P = \frac{PMT}{r} \left(1 - \frac{1}{(1 + r)^n}\right)$, where $P$ is the loan amount, $PMT$ is the annual payment, $r$ is the annual interest rate, and $n$ is the number of payments. Rearranging to solve for $PMT$, we get $PMT = \frac{P \cdot r}{1 - \frac{1}{(1 + r)^n}}$.Given: $P = \$12,000$, $r = 14\% = 0.14$, and $n = 6$.$PMT = \frac{\$12,000 \cdot 0.14}{1 - \frac{1}{(1 + 0.14)^6}} \approx \$2,948.22$.The balance after the second payment can be found by updating the loan amount for two payments and then subtracting the payments made. This is equivalent to calculating the present value of the remaining 4 payments:$Balance = \frac{\$2,948.22}{0.14} \left(1 - \frac{1}{(1 + 0.14)^4}\right) \approx \$9,258.80$.The interest for the third payment is $14\%$ of this balance:Interest = $0.14 \times \$9,258.80 \approx \$1,258.80$.

Question 11

A $60,000 loan at 12% compounded semi-annually is to be repaid by monthly payments of $1,000.
-How long will it take to pay off this loan?

Accepted Answer

The loan is compounded semi-annually, so the effective annual rate is slightly higher than 12%. Monthly payments of $1,000 will take approximately 7 years and 7 months to pay off the loan when considering the compounding effect.

Question 12

An $80,000 loan is amortized by monthly payments over 25 years. The interest rate charged is 10% compounded semi-annually.
-A $3100 item is paid for by end-of-month payments of $350. The interest rate charged is 15% compounded monthly. What is the size of the final payment?

Accepted Answer

The correct answer is A because the final payment is the unpaid balance of the loan, which is $158.46.

Question 13

A $13,000 loan is to be amortized by equal monthly payments for five years. The interest rate is 12% compounded monthly.
-How much will the debtor owe after two years (just after the payment is made at the end of two years)?

Accepted Answer

The answer of A $13,000 loan is to be amortized...

Question 14

A $60,000 loan at 12% compounded semi-annually is to be repaid by monthly payments of $1,000.
-What is the size of the final payment?

Accepted Answer

The answer of  A $60,000 loan at 12% compounded...

Question 15

An $80,000 loan is amortized by monthly payments over 25 years. The interest rate charged is 10% compounded semi-annually.
-What will the principal balance be after three years?

Accepted Answer

The correct answer is A because the principal balance after three years is $77,400.72.

Question 16

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?

Accepted Answer

The interest included in the first payment is the interest accrued during the first month. The monthly interest rate is 6% / 12 = 0.5%. The interest accrued during the first month is $32,000 * 0.5% = $156.

Question 17

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?

Accepted Answer

The answer of A $67,800 loan is to be repaid...

Question 18

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. How much interest will be included in the first payment?

Accepted Answer

The monthly interest rate is 7.2%/12 = 0.6%. The interest for the first month is 0.6% of $17,355, which is $104.13, rounded to $104.

Question 19

An $80,000 loan is amortized by monthly payments over 25 years. The interest rate charged is 10% compounded semi-annually.
-How much interest will be paid during the first three years?

Accepted Answer

The answer of An $80,000 loan is amortized by monthly...

Question 20

A $13,000 loan is to be amortized by equal monthly payments for five years. The interest rate is 12% compounded monthly.
-How much interest will the debtor pay in total over the five-year period?

Accepted Answer

To find the total interest paid, first calculate the monthly payment using the formula for an amortizing loan. Then, multiply the monthly payment by the total number of payments (60) and subtract the principal ($13,000) from this total to find the interest paid. The correct total interest paid is $4350.80.

Quiz 13: Loan Amortization: Mortgages

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 included in the first payment?

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?

A $60,000 loan at 12% compounded semi-annually is to be repaid by monthly payments of $1,000. -How much will the principal be reduced by payments 13 to 24 inclusive?

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?

Miss Jones borrowed $10,000 at 12% compounded monthly, and agreed to pay back the loan by equal monthly payments over five years. After making the first 10 payments on time, she missed the next four payments. -How much extra interest did Miss Jones have to pay because of the late payments?

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

A loan of $12,000 with interest at 14% compounded annually is to be amortized by equal payments at the end of each year for six years. -What is the outstanding principal just after the fifth payment?

A loan of $12,000 with interest at 14% compounded annually is to be amortized by equal payments at the end of each year for six years. -How much interest is included in the third payment?

A $60,000 loan at 12% compounded semi-annually is to be repaid by monthly payments of $1,000. -How long will it take to pay off this loan?

An $80,000 loan is amortized by monthly payments over 25 years. The interest rate charged is 10% compounded semi-annually. -A $3100 item is paid for by end-of-month payments of $350. The interest rate charged is 15% compounded monthly. What is the size of the final payment?

A $13,000 loan is to be amortized by equal monthly payments for five years. The interest rate is 12% compounded monthly. -How much will the debtor owe after two years (just after the payment is made at the end of two years) ?

A $60,000 loan at 12% compounded semi-annually is to be repaid by monthly payments of $1,000. -What is the size of the final payment?

An $80,000 loan is amortized by monthly payments over 25 years. The interest rate charged is 10% compounded semi-annually. -What will the principal balance be after three years?

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?

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?

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. How much interest will be included in the first payment?

An $80,000 loan is amortized by monthly payments over 25 years. The interest rate charged is 10% compounded semi-annually. -How much interest will be paid during the first three years?

A $13,000 loan is to be amortized by equal monthly payments for five years. The interest rate is 12% compounded monthly. -How much interest will the debtor pay in total over the five-year period?