Calculate the following information for a $50,000 loan with four (4) annual payments that have a...

Calculate the following information for a $50,000 loan with four (4) annual payments that have a variable interest rate each year.

In year 1, the interest rate is 9.50%.
In year 2, the interest rate is 8.75%.
In year 3, the interest rate is 11.50%.
In year 4, the interest rate is 5.00%

In order for your answers to be marked correct by Canvas, remember to include dollar signs ($), commas for each thousand (000) dollars, and to the nearest whole cent.

Year	Total Payment	Interest	Principal	Loan Balance
0
1
2
3
4				$0

Solutions

Expert Solution


We can use the present value of annuity formula to calculate the loan annual payment
Present value of annuity = P x {[1 - (1+r)^-n]/r}
Present value of annuity = Loan amount , r = interest rate per annum ,n = number of years and P = annual loan payment

Year 1 - Annual Loan payment					Year 2 - Annual Loan payment
Present value of annuity = $50000					Present value of annuity = loan balance at the end of 1st Year = $39146.85
r = interest rate per annum = 9.50%					r = interest rate per annum = 8.75%
n = number of years = 4					n = number of years = 3
P = annual loan payment = ?					P = annual loan payment = ?
50000 = P x {[1 - (1+0.095)^-4]/0.095}					39146.85 = P x {[1 - (1+0.0875)^-3]/0.0875}
50000 = P x 3.204481					39146.85 = P x 2.5426156
P = 15603.15					P = 15396.29
Annual Loan payment in First Year = $15,603.15					Annual Loan payment in Second Year = $15,396.29

Year 3 - Annual Loan payment
Present value of annuity = loan balance at the end of 2nd Year = $27,175.91
r = interest rate per annum = 11.50%
n = number of years = 2
P = annual loan payment = ?
27175.91 = P x {[1 - (1+0.115)^-2]/0.115}
27175.91 = P x 1.701221
P = 15974.36
Annual Loan payment in third Year = $15,974.36

Year	Total Payment	Interest	Principal	Loan balance
0				$50,000.00
1	$15,603.15	$4,750.00	$10,853.15	$39,146.85
2	$15,396.29	$3,425.35	$11,970.94	$27,175.91
3	$15,974.36	$3,125.23	$12,849.13	$14,326.78
4	$15,043.12	$716.34	$14,326.78	$0.00

jeff jeffy answered 1 year ago

Next > < Previous

Related Solutions

Consider a $12,000 loan with 4 equal annual payments and 10% interest. a. Calculate the annual...

Consider a $12,000 loan with 4 equal annual payments and 10% interest. a. Calculate the annual payment, n = 4, r = 0.10. b. Prepare a complete loan payment schedule table for this loan. You need the time period, the beginning principal, payment, interest paid, principal paid, and ending principal in your table. c. Now assume that the loan is fully amortized over 4 years, however, the interest rate is variable. That is, the bank changes a different rate each...

You have a 10 year loan for $50,000 and you make annual payments. The interest rate...

You have a 10 year loan for $50,000 and you make annual payments. The interest rate is 6% annual compounded quarterly. a) What are your annual payments? b) If the inflation rate is 3.2% annual compounded monthly, what is the purchasing power of your final payment in year 2 dollars? c) What are the equal annual payments in year 2 constant dollars with the above inflation rate? d) What is the total interest paid in year 2 constant dollars with...

You have a loan outstanding. It requires making four annual payments of $8,000 each at the...

You have a loan outstanding. It requires making four annual payments of $8,000 each at the end of the next four years. Your bank has offered to restructure the loan so that instead of making the four payments as originally agreed, you will make only one final payment in four years. If the interest rate on the loan is 9%, what final payment will the bank require you to make so that it is indifferent to the two forms of...

A man has a loan of 50,000 for 10 years ay 6.5% annually with annual payments....

A man has a loan of 50,000 for 10 years ay 6.5% annually with annual payments. His payments are 4500 for the first 5 years and X for the next 5 years. Find X.

You have a loan outstanding. It requires making six annual payments of $ 4 comma 000...

You have a loan outstanding. It requires making six annual payments of $ 4 comma 000 each at the end of the next six years. Your bank has offered to allow you to skip making the next two payments in lieu of making one large payment at the end of the loan's term in six years. If the interest rate on the loan is 10 %, what final payment will the bank require you to make so that it is...

$100,000 Amortizing Loan 9% Stated Rate 20 Year amortization Annual payments -Calculate annual payments - Prepare...

$100,000 Amortizing Loan 9% Stated Rate 20 Year amortization Annual payments -Calculate annual payments - Prepare amortization table

4. Calculate the payments and amortization table of a 3-year car loan for $12,000 at a...

4. Calculate the payments and amortization table of a 3-year car loan for $12,000 at a 6% rate of interest. The loan will be repaid with three annual payments.

Given a loan with the following characteristics: Co = 50,000€ Annual effective interest 6% to be...

Given a loan with the following characteristics: Co = 50,000€ Annual effective interest 6% to be amortized in 6 years, and knowing it is a level-fixed payment-rate loan. Just before making the payment of the second annuity, it is decided to change the amortization method, starting to be amortized through constant principal repayments loan. a) Outstanding debt just after making the payment of the 3th annuity b) Amortization schedule for the last 3 years

Fred is repaying a loan of X at a 4% annual effective rate. He makes payments...

Fred is repaying a loan of X at a 4% annual effective rate. He makes payments of 100 at the end of each year for 10 years, followed by payments of 200 for n years. The amount of interest in the 8th payment is 60. Determine X. Possible answers are: 1,140 or 1,970 or 1,360 or 1,740 or 1,870. Thanks

A loan of €50,000 is being repaid with monthly level payments at the end of each...

A loan of €50,000 is being repaid with monthly level payments at the end of each year for 6 years at 5% effective rate. Just after making the payment of the second annuity, it is decided to change the amortization method, the loan is being repaid with constant annual principal repayments for the remaining 3 years at an interest rate of 4.5%. A) find the outstanding debt just after the payment of the third annuity

Subjects