Question

Your business has just taken out a 1-year installment loan for $72,500 at a nominal rate of 6.5% but with equal end-of-month payments. What percentage of the 2nd monthly payment will go toward the repayment of principal?

Select the correct answer.

a. 94.23%

b. 96.23%

c. 98.23%

d. 95.23%

e. 97.23%

Answer 1

The % is computed as shown below:

The monthly payment is computed as shown below:

Present value = Monthly payment x [ (1 – 1 / (1 + r)ⁿ) / r ]

r is computed as follows:

= 6.5% / 12 (Since the payments are monthly, hence divided by 12)

= 0.541666667% or 0.00541666667

So, the monthly payment will be computed as follows:

$ 72,500 = Monthly payment x [ (1 - 1 / (1 + 0.00541666667)¹² ) / 0.00541666667]

Monthly payment = $ 6,256.490614

Amortization table is presented as follows:

Month	Beginning Balance	Monthly Payment	Interest	Principal	Ending Balance
1	$ 72,500	$ 6,256.490614	= $ 72,500 x 6.5% / 12 = $ 392.7083333	= $ 6,256.490614 - $ 392.7083333 = $ 5,863.782281	= $ 72,500 - $ 5,863.782281 = $ 66,636.21772
2	$ 66,636.21772	$ 6,256.490614	= $ 66,636.21772 x 6.5% / 12 = $ 360.9461793	= $ 6,256.490614 - $ 360.9461793 = $ 5,895.544435	= $ 66,636.21772 - $ 5,895.544435 = $ 60,740.67329

So, the % will be as follows:

= Principal amount of 2nd month / 2nd month monthly payment

=  $ 5,895.544435 / $ 6,256.490614

= 94.23% Approximately

So, the correct answer is option a.

Please ask in case of any query.