Question

Gerald has taken out a loan of $100,000 today to start a business. He has agreed to repay the loan on the following terms:

• Repayments will be made on a monthly basis. The first repayment will be made exactly one month from today.

• The repayments for the first 5 years will cover interest only to help reduce the financial burden for Gerald’s business at the start.

• After the 5-year interest-only period, Gerald will make level monthly payments that will fully repay the loan after an additional 15 years (i.e. 20 years from today, the loan will be fully repaid).

• The interest charged is 5% p.a. effective.

10 years have passed, and Gerald’s business is doing well. Further, he has made all the repayments on his loan so far as described above, and has just made the repayment due today. However, it has just been announced that the interest rate on Gerald’s loan will go up to 5.5% p.a. compounding semi-annually.

d) Calculate the new equivalent effective monthly rate on the loan.

e) Calculate the current loan outstanding (again, it is 10 years after the loan was initially taken out). Note that the new interest rate only applies from today onwards.

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f) Because Gerald’s business is doing well, he decides to repay a lump sum of $10,000 immediately. To further reduce the amount of interest he is paying to the bank, he will increase his monthly repayments to $1,000 per month

Answer 1

Initially amount of loan taken by Gerald			$100,000
Interest rate for initially 5 years
After the initially 5 years lapsed amount of installment to cover the fully outstanding amount
Outstanding amount	= $100000	(As the only interest is paid in initially 5 years period)
Interest Rate p.a	= 5%
Repayment period	= 15 Years

Equal installment for 15 years
		= No of Month
		= 15 * 12 = 180 ( No of installment)
		= Installment amount= ( Principal + interest)
	Principal amount	$ 100000
	Interest rate	5% P.a
	Tenure no of Month	180 Month
	EMI Payment	= Principal * rate of inierest *	( 1+ rate of interest)no of Tenure
				( 1+ rate of interest)no of Tenure - 1
		=    100000*0.00416667*	(1+0.0041667)power to 180
				(1+0.0041667)power to 180 -1
		=     416.6667	+      (1.00416667)power to 180
		=	(1.00416667)power to 180 -1
		= 416.6667	+2.11371
			+2.11371-1
		=$ 790.9 per Month
	Calculation of outstanding amount at the end to 10 years
	installment payment for next 5 year	= $791*(5 years*12)
			= $47460
	Outstanding principal amount at the end of 10 years
		=$100000- $47460
		=   $52540