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

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

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