Question

Joe borrowed $8 million to purchase an apartment in Melbourne. The loan requires monthly repayments over 19 years. The interest rate of the borrowing was 6.2 per cent per annum, but 3 years later the bank increased the interest rate by 1.7 per cent per annum, in line with market rates. The bank manager tells Joe that his monthly repayment will increase to pay off the loan by the originally agreed date. Calculate the new monthly repayment.

Answer 1

Original payments:

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                       8,000,000
Rate of interest per period:
Annual rate of interest		6.200%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.062 /12 =	0.5167%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	19.00
Total number of payments	N	19 × 12 =	228
Period payment using the formula	=	[ 8000000 × 0.00517 × (1+0.00517)^228] / [(1+0.00517 ^228 -1]
Monthly payment	=	$                                                      59,801.90

Loan balance after three years

Loan balance	=	PV * (1+r)^n - P[(1+r)^n-1]/r
Loan amount	PV =	8,000,000.00
Rate of interest	r=	0.5167%
nth payment	n=	36
Payment	P=	59,801.90
Loan balance	=	8000000*(1+0.00517)^36 - 59801.9*[(1+0.00517)^36-1]/0.00517
Loan balance	=	7,271,341.23

New monthly payment:

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                       7,271,341
Rate of interest per period:
Annual rate of interest		7.900%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.079 /12 =	0.6583%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	16.00
Total number of payments	N	16 × 12 =	192
Period payment using the formula	=	[ 7271341.23 × 0.00658 × (1+0.00658)^192] / [(1+0.00658 ^192 -1]
Monthly payment	=	$                                                      66,828.55

Answer is $66,828.55

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