Question

Fiona takes out a $400 000 home loan over 30 years. Her monthly repayments are set at $2171.80.

a) Find the annual interest rate, compounded monthly (express answer in % to 2 decimal places). [3]

b) Find the outstanding balance of the loan after 10 years. [3]

c) After 10 years, Fiona transfers the remainder of the loan to a bank charging 4.73% p.a. interest compounded monthly. Assume that the term of the loan remains 30 years.

(i) Calculate the new monthly repayment. [3]

(ii) How much interest will Fiona save by refinancing the loan?

Answer 1

a

Interest rate is 5.10% APR monthly compounding. At this rate monthly payment is 2171.80

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                          400,000
Rate of interest per period:
Annual rate of interest		5.100%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.051 /12 =	0.4250%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	30.00
Total number of payments	N	30 × 12 =	360
Period payment using the formula	=	[ 400000 × 0.00425 × (1+0.00425)^360] / [(1+0.00425 ^360 -1]
Monthly payment	=	$                                                         2,171.80

b

Loan balance	=	PV * (1+r)^n - P[(1+r)^n-1]/r
Loan amount	PV =	400,000.00
Rate of interest	r=	0.4250%
nth payment	n=	120
Payment	P=	2,171.80
Loan balance	=	400000*(1+0.00425)^120 - 2171.8*[(1+0.00425)^120-1]/0.00425
Loan balance	=	326,344.53

Balance after ten years is $326,344.53

c

New loan
Rate	4.73%
Period	240
Loan amount	$      326,344.53
Monthly payment	$           2,105.35

d

Interest savings:
Old loan balance payments	521,232.00
Less: new loan total payments	505,284.00
Interest savings	15,948.00