Question

Jim needs to borrow $125,500 for a business expansion project. His bank agrees to lend him the money over a 4-year term at an APR of 4% and will accept either annual, or monthly payments with no change in the quoted APR.

a. Calculate the periodic payment under

each alternative (monthly and annual payments). For each alternative, you have to do the following:

                                          

i.     Plug in the values in the formula                                 

ii.     Get the PMT in the calculator. Make sure you show me the keys you enter.                                          

iii.     Write the formula and arguments using Excel format.

b.     Compare the total amount paid each year

under each option. What option would you choose? Why?

Formula:

Answer 1

Monthly option:

Input		Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
		Using the formula:
PV		Loan amount	P	$                                                          125,500
		Rate of interest per period:
		Annual rate of interest		4.000%
		Frequency of payment	=	Once in 1 month period
		Numer of payments in a year	=	12/1 =	12
I=		Rate of interest per period	R	0.04 /12 =	0.3333%
		Total number of payments:
		Frequency of payment	=	Once in 1 month period
		Number of years of loan repayment	=	4
N=		Total number of payments	N	4 × 12 =	48
		Period payment using the formula	=	[ 125500 × 0.00333 × (1+0.00333)^48] / [(1+0.00333 ^48 -1]
PMT		Monthly payment	=	$                                                         2,833.67

Monthly payment is 2,833.67

Annual payment:

Input		Monthly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
		Using the formula:
PV		Loan amount	P	$                                                          125,500
		Rate of interest per period:
		Annual rate of interest		4.000%
		Frequency of payment	=	Once in 12 month period
		Numer of payments in a year	=	12/12 =	1
I=		Rate of interest per period	R	0.04 /1 =	4.0000%
		Total number of payments:
		Frequency of payment	=	Once in 12 month period
		Number of years of loan repayment	=	4
N=		Total number of payments	N	4 × 1 =	4
		Period payment using the formula	=	[ 125500 × 0.04 × (1+0.04)^4] / [(1+0.04 ^4 -1]
PMT		Monthly payment	=	$                                                      34,574.00

Yearly payment is 34,574

Monthly payment is better as earlier payment reduces pricipal first paying less total interest.

Please rate.