Question

Kimiko signed a mortgage requiring payments of $407.95 at the end of every month for 4 years at 6.2 % compounded monthly.

(a) How much was the original mortgage balance?

(b) If Kimiko missed the first 8 payments, how much would she have to pay after 9 months to bring the mortgage payments up to date?

(c) How much would Kimiko have to pay after 9 months to pay off the mortgage (assuming she missed all the payments)?

(d) If the mortgage were paid off after 9 months, what would the total interest cost be?

(e) How much of the total interest cost is additional interest because of the missed payments?

Answer 1

a

a	Present value of annuity=	P* [ [1- (1+r)-n ]/r ]
P=	Periodic payment	407.95
r=	Rate of interest per period
	Annual interest	6.20%
	Number of payments per year	12
	Interest rate per period	0.062/12=
	Interest rate per period	0.517%
n=	number of periods:
	Number of years	4
	Periods per year	12
	number of payments	48
	Present value of annuity=	407.95* [ (1- (1+0.00517)^-48)/0.00517 ]
	Present value of annuity=	17,303.00

Original mortgage is 17,303

b

Future value	FV=	PV * (1+rs/m)^mN
Present value	PV=	17,303
Stated rate of interest	rs=	6.20000%
Number of years	N=	0.75
Frequency of compounding per year	m=	12
Future value	FV=	17303 *(1+ 0.062/12)^(0.75*12)
	FV=	18,124.42

Total payment = 18124.42

c

Interest = 18,124.42 - 17303 = 821.42

d

Calculator
Inputs:
PV	17,303.00
PMT	($407.95)
Rate (I/Y)	0.517%
Term N	9.00
Output:
FV	($14,356.70)
Principal paid	2,946.30
Total payments	3671.55
Interest paid	725.25
Interest with penalty	821.42
Additional interest paid	96.17

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