Question

Samuel and Sandra Sharp wish to borrow $600,000 to buya home. The loan from the Highway Bank requires equal monthly repayments over 20 years, and carries an interest rate of 5-1 % per annum, compounded monthly. The first repayment is due at the end of one month after the loan proceeds are received. You are required to calculate the following. i) The effective annual interest rate on the above loan (show as a percentage correct to 3 decimal places). li) The amount of the monthly repayment (consisting of interest and principal repayment components) if the same amount is to be repaid every month over the 20 year period of the loan. ii) The amount of SK, if - instead of the above - the Highway Bank agrees that Samuel and Sandra will repay the loan bypaying the bank $3.200 per month for the first 12 months, then $3,600 a month for the next 12 months, and after that SK per month for the balance of the 20 year term. iv) How long (in years and months) from inception will it take to repay the loan if, alternatively, Samuel and Sandra decide to repay $4,500 per month, with the first repayment now being at the end of the thirteenth month after taking the loan, and continuing until the loan is repaid? HINTS A. The final repayment is likely to be less than $4,500 and will be paid one month after the final full instalment of $4,500 is paid. B. While no repayments will be made during the first 12 months, interest will be charged by Highway Bank at the stipulated rate.]

Answer 1

1)
Effective Interest Rate = Effective(5.1%,12)	5.221%
Alternative Method
Effective Interest Rate = [(1+5.1%/12)^12]-1	5.221%
2)
Principal	$600,000.00
Rate = 5.1%/12	0.43%
Period = 20 x 12	240
Monthly Payment = PMT(.43%,240,-600000)	$3,992.95
3)
Loan balance after 18 years = $600,000 - (3200 x 12) - (3600 x 12)	$ 518,400.00
Rate = 5.1%/12	0.43%
Period = 18 x 12	216
Monthly Payment = PMT(.43%,216,-518400)	$3,672.58
4)
Principal = 600000 x 1.051	$630,600.00
Rate = 5.1%/12	0.43%
Monthly Payment =	$4,500.00
NPER = NPER(.43%,4500,-630600)	213.45663627
Period for repayment	17.79	years