Question

Your company is planning to borrow $3 million on a 5-year, 13%, annual payment, fully amortized term loan. What fraction of the payment made at the end of the second year will represent repayment of principal? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

Yearly payment	=	[P × R × (1+R)^N ] / [(1+R)^N -1]
Using the formula:
Loan amount	P	$                                                       3,000,000
Rate of interest per period:
Annual rate of interest		13.0000000%
Frequency of payment	=	Once in 12 month period
Numer of payments in a year	=	12/12 =	1
Rate of interest per period	R	0.13 /1 =	13.0000%
Total number of payments:
Frequency of payment	=	Once in 12 month period
Number of years of loan repayment	=	5.00
Total number of payments	N	5 × 1 =	5
Period payment using the formula	=	[ 3000000 × 0.13 × (1+0.13)^5] / [(1+0.13 ^5 -1]
Yearly payment	=	$                                                    852,943.63

Period	Beginning liability	Uniform monthly payment	Interest owed	Principal payment	Total owed at end of month
N	A	C	B= A* 0.130000	D=C-B	E=A-D
1	3,000,000.00	852,943.63	390,000.00	462,943.63	2,537,056.37
2	2,537,056.37	852,943.63	329,817.33	523,126.30	2,013,930.07

Fraction =

523,126.30 / 852,943.63

= 61.33%

Answer is:

61.33%

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