Question

Question 1

I. You plan to borrow $35,000 at an 8% annual interest rate. The terms require you to amortize the loan with 6 equal end-of- year payments. a) Calculate the amount of annual payment you would be paying every year? b) Set-up an amortization schedule.   

II. Allied Bank offers to lend you at a nominal rate of 5.0%, simple interest, with interest paid quarterly. Standard Bank offers to lend you the same amount, but it will charge 6.0%, simple interest, with interest paid at the end of the year. Which bank will you select to borrow money?

III. Your uncle has $500,000 invested at 5.5%, and he now wants to retire. He wants to withdraw $50,000 at the beginning of each year, beginning immediately. He also wants to have $45,000 left to give you when he ceases to withdraw funds from the account. For how many years can he make the $50,000 withdrawals and still have $45,000 left in the end? (First make a time-line indicating inflows and outflows and then calculate for the asked output). Hint: your uncle has $500,000 therefore, it's an inflow.   

Answer 1

I]
a]	Annual payments = 35000*0.08*1.08^6/(1.08^6-1) =	$                7,571
b]	Year	Beginning Balance	Interest	Installment	Payment towards principal	Ending Balance
	1	$              35,000	$                  2,800	$          7,571	$        4,771	$       30,229
	2	$              30,229	$                  2,418	$          7,571	$        5,153	$       25,076
	3	$              25,076	$                  2,006	$          7,571	$        5,565	$       19,511
	4	$              19,511	$                  1,561	$          7,571	$        6,010	$       13,501
	5	$              13,501	$                  1,080	$          7,571	$        6,491	$          7,010
	6	$                7,010	$                     561	$          7,571	$        7,010	$                  0
II]	Allied bank effective rate = (1+0.05/4)^4-1 =	5.09%
	Standard bank effective rate	6.00%
	Allied bank will be selected to borrow money as it
	offers the lower effective interest rate.
III]	The equality is,
	500000 = 50000*PVIFA(5.5,n)+45000*PVIF(5.5,n)
	The value of n is to be found out by trial and error.
	Using n = 14
	The value of RHS = 50000*9.58965+45000*0.47257 =	$            500,748
	Using n = 13
	The value of RHS = 50000*9.11708+45000*0.49856 =	$            478,289
	n = 13+(500000-478289)/(500748-478289) =	13.97
	Number of years for which withdrawal can be made =	14	Years