Question

1.Find the monthly payments on a $178,000 15 year mortgage assuming i(2)=6.7%.

2.Find the present value of a perpituity paying $590 at the end of each year assuming interest rates are i(1)=3.6%  and the first payment is in 1 year.

3.Find the present value of an annuity paying $650 per month for 10 years assuming i(4)=14%.

4.

Answer 1

1

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                          178,000
Rate of interest per period:
Annual rate of interest		6.700%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.067 /12 =	0.5583%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	15
Total number of payments	N	15 × 12 =	180
Period payment using the formula	=	[ 178000 × 0.00558 × (1+0.00558)^180] / [(1+0.00558 ^180 -1]
Monthly payment	=	$                                                         1,570.21

2

Present value of perpetuity = 590/3.6% = 16,388.89

3

a	Present value of annuity=	P* [ [1- (1+r)-n ]/r ]
P=	Periodic payment	650.00
r=	Rate of interest per period
	Annual interest	14.00%
	Number of payments per year	12
	Interest rate per period	0.14/12=
	Interest rate per period	1.167%
n=	number of periods:
	Number of years	10
	Periods per year	12
	number of payments	120
	Present value of annuity=	650* [ (1- (1+0.01167)^-120)/0.01167 ]
	Present value of annuity=	41,863.52

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