Question

Suppose you have an interest only loan for $30,000 over 5 years. Should the interest rate be an APR of 7%, compounded monthly, what is the monthly payment in all but the final month?

Consider an annuity that pays equal monthly payments of $600 for the next 30 years. Given this, and an APR of 5%, compounded monthly, what would you pay for this today?

Answer 1

First part:

Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                            30,000
Rate of interest per period:
Annual rate of interest		7.000%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.07 /12 =	0.5833%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	5
Total number of payments	N	5 × 12 =	60
Period payment using the formula	=	[ 30000 × 0.00583 × (1+0.00583)^60] / [(1+0.00583 ^60 -1]
Monthly payment	=	$                                                            594.04

Monthly payment on loan is 595.04

Second part:

a	Present value of annuity=	P* [ [1- (1+r)-n ]/r ]
P=	Periodic payment	600.00
r=	Rate of interest per period
	Annual interest	5.00%
	Number of payments per year	12
	Interest rate per period	0.05/12=
	Interest rate per period	0.417%
n=	number of periods:
	Number of years	30
	Periods per year	12
	number of payments	360
	Present value of annuity=	600* [ (1- (1+0.00417)^-360)/0.00417 ]
	Present value of annuity=	111,768.97

Amount that can be paid today is $111,768.97

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