Question

Rico needs approximately $2,400 to buy a new computer. A​ two-year unsecured loan through the credit union is available for 11.25 percent interest. The current rate on his revolving home equity line is 8.00 ​percent, although he is reluctant to use it. Rico is in the 15 percent federal tax bracket and the 5.75 percent state tax bracket. Which loan should he​ choose? Why? Regardless of the loan​ chosen, Rico wants to pay off the loan in 24 months. Calculate the monthly payments for​ him, assuming both loans use the simple interest calculation method.

The​ after-tax cost of the home equity loan is ​%

Answer 1

Total tax rate applicable is = federal tax rate + state tax rate = 15% + 5.75% = 20.75%

After tax cost of home equity loan = Home equity loan rate X ( 1 - tax rate) = 8% X (1- 20.75%) = 6.34%

After tax cost of home equity loan is 6.34%

Monthly payments:

If loan is taken from credit union:

Monthly payment	=	[P * R * (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	2,400.00
Rate of interest per period:
Annual rate of interest		11.250%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.1125 /12 =	0.9375%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	2
Total number of payments	N	2*12 =	24
Period payment using the formula	=	[ 2400*0.00938*(1+0.00938)^24] / [(1+0.00938 ^24 -1]
Monthly payment	=	112.14

When home equity loan taken then monthly payment is:

Monthly payment	=	[P * R * (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	2,400.00
Rate of interest per period:
Annual rate of interest		8.000%
Frequency of payment	=	Once in 1 month period
Numer of payments in a year	=	12/1 =	12
Rate of interest per period	R	0.08 /12 =	0.6667%
Total number of payments:
Frequency of payment	=	Once in 1 month period
Number of years of loan repayment	=	2
Total number of payments	N	2*12 =	24
Period payment using the formula	=	[ 2400*0.00667*(1+0.00667)^24] / [(1+0.00667 ^24 -1]
Monthly payment	=	108.55