Question

1. Your company has just taken out a 3-years installment loan for $1,000 at a nominal rate of 10.0% with equal end-of-month payments $402.11. What is the beginning balance, Interest, Principal, and Ending balance for the year two and three?

Answer 1

We can use PV of an Annuity formula to calculate the annual payment

PV = PMT * [1-(1+i) ^-n)]/i

Where PV (present value of loan) = $1,000

PMT = Annual payment =?

n = N = number of payments = 3

i = I/Y = interest rate per year = 10%

Therefore,         

$1,000 = PMT* [1- (1+10%) ^-3]/10%

PMT = $402.11

Therefore as given in the question; equal end-of-year payments on loan is $402.11        

We can make amortization schedule in following manner to know the beginning balance, Interest, Principal, and Ending balance for the year two and three.

Loan amount	$1,000.0
Annual payment =	$402.11
Interest rate =	10%
Time period	3
Amortization Schedule
Year	Beginning Balance	Total payment (PMT)	Interest Payment @ 10% of beginning balance	Principal payment (Total Payment - Interest)	Ending Balance (Beginning balance - Principal Payment)
1	$1,000.0	$402.11	$100.00	$302.11	$697.89
2	$697.89	$402.11	$69.79	$332.33	$365.56
3	$365.56	$402.11	$36.56	$365.56	$0.00