Question

Consider a $50,000 loan to be repaid in equal installments at the end of each of the next 5 years. The interest rate is 10%.

1. Set up an amortization schedule for the loan. Round your answers to the nearest cent. Enter "0" if required

   Year	Payment	Repayment Interest	Repayment of Principal	Balance
   1	$	$	$	$
   2	$	$	$	$
   3	$	$	$	$
   4	$	$	$	$
   5	$	$	$	$
   Total	$	$	$

   
   
2. How large must each annual payment be if the loan is for $100,000? Assume that the interest rate remains at 10% and that the loan is still paid off over 5 years. Round your answer to the nearest cent.
   $    
   
3. How large must each payment be if the loan is for $100,000, the interest rate is 10%, and the loan is paid off in equal installments at the end of each of the next 10 years? This loan is for the same amount as the loan in part b, but the payments are spread out over twice as many periods. Round your answer to the nearest cent.
   $    

Answer 1

Answer a

Present value of Annuity = A*[(1-(1+r)^-n)/r]

Where

A - Annuity payment = ?

r - rate per period = 10%

n - no. of periods = 5

50000 = A* [(1-(1+.10)^-5)/.10]

= A* [(1-0.62092132305)/.10]

= A*3.7907867695

A = 50000/3.7907867695

= 13189.87

Year	Opening Balance	Total Payment	interest paid	principal paid	end balance
1	50000.00	13189.87	5000.00	8189.87	41810.13
2	41810.13	13189.87	4181.01	9008.86	32801.27
3	32801.27	13189.87	3280.13	9909.74	22891.53
4	22891.53	13189.87	2289.15	10900.72	11990.81
5	11990.81	13189.87	1199.08	11990.81	0.00

Interest paid = Opening Balance*10%/12

Principal paid = Total Payment - Interest paid

End balance = Opening Balance - Principal paid

Answer b

Present value of Annuity = A*[(1-(1+r)^-n)/r]

Where

A - Annuity payment = ?

r - rate per period = 10%

n - no. of periods = 5

100000 = A* [(1-(1+.10)^-5)/.10]

= A* [(1-0.62092132305)/.10]

= A*3.7907867695

A = 100000/3.7907867695

= 26379.75

Answer c

Present value of Annuity = A*[(1-(1+r)^-n)/r]

Where

A - Annuity payment = ?

r - rate per period = 10%

n - no. of periods = 10

100000 = A* [(1-(1+.10)^-10)/.10]

= A* [(1-0.38554328943)/.10]

= A*6.1445671057

A = 100000/6.1445671057

= 16274.54