Student borrowers now have more options to choose from when selecting repayment plans. The ‘Standard’ plan...

Student borrowers now have more options to choose from when selecting repayment plans. The ‘Standard’ plan repays the loan up to 10 years with equal monthly payments. The ‘Extended’ plan allows up to 25 years to repay the loan. Assume that a student borrows $55,000 at 4.66% interest compounded monthly. (Source: U.S. Ministry of Education)

Construct an Amortization Schedule under the ‘Standard’ plan over 10 years

((a)

(i) Find the monthly payment

(ii) What is the total interest paid over the 10 years

(iii) How much of the 5^th payment is used to reduce the loan?

(b) Construct an Amortization Schedule under the ‘Extended’ plan over 25 years (14 points)

(i) Find the monthly payment

(ii) What is the total interest paid over the 25 years

(iii) How much of the 5^th payment is used to reduce the loan?

Expert Solution


(a)	Standard Plan -
	Loan amount =		55000
	Interest Rate =		4.66% p.a.	0r 4.66/12 =	0.3883%	Monthly compounding
	Term of loan =		10 Years or	10 x 12months =	120
	Payment -		Monthly

	(i)	Monthly payments =		Loan/ Annuity factor(interest,term)
		PVAF(0.3883%,120) =			95.7750
		Monthly payments =		55000/95.775 =	574.2628

	(ii)	Total Interest paid over the term of loan =
		Total amount paid for loan = Installment x No of installments
				= 574.2628 x 120
					68911.53
		Less: Principle amount of loan			55000
		Total Interest paid			13911.53

	(iii)	It means what is the principle amount of loan in 5th installment
	Month	Beginning balance	Installments	Interest	Principle	Closing balance
	1	2	3	4 = 2 x 0.3883%	5 = 3 - 4	6 = 2 -5

	1	55000	574.2628	213.5833	360.6794	54639.32
	2	54639.32	574.2628	212.1827	362.0801	54277.24
	3	54277.24	574.2628	210.7766	363.4861	53913.75
	4	53913.75	574.2628	209.3651	364.8977	53548.86
	5	53548.86	574.2628	207.9481	366.3147	53182.54

	Principle amount in 5th installmet =					366.3147


(b)	Extended plan -
	Loan amount =		55000
	Interest Rate =		4.66% p.a.	0r 4.66/12 =	0.3883%	Monthly compounding
	Term of loan =		25 years or	25 x 12months =	300
	Payment -		Monthly

	(i)	Monthly payments =		Loan/ Annuity factor(interest,term)
		PVAF(0.3883%,300) =			177.0059
		Monthly payments =		55000/177.0059 =	310.7242

	(ii)	Total Interest paid over the term of loan =
		Total amount paid for loan = Installment x No of installments
				= 310.7242 x 300
					93217.25
		Less: Principle amount of loan			55000
		Total Interest paid			38217.25

	(iii)	It means what is the principle amount of loan in 5th installment
	Month	Beginning balance	Installments	Interest	Principle	Closing balance
	1	2	3	4 = 2 x 0.3883%	5 = 3 - 4	6 = 2 -5

	1	55000	310.7242	213.5833	97.14083	54902.86
	2	54902.86	310.7242	213.2061	97.51806	54805.34
	3	54805.34	310.7242	212.8274	97.89676	54707.44
	4	54707.44	310.7242	212.4472	98.27692	54609.17
	5	54609.17	310.7242	212.0656	98.65856	54510.51

	Principle amount in 5th installmet =					98.65856

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