Question

Applies TVM techniques to real problems Peter is considering making a loan of $500,000 to Paul. It is a three-year loan with annual payments due at the end of each year and a 7% annual interest rate. Find the payments that would be required to amortize the loan over the three-year period and then prepare an amortization schedule to demonstrate how the loan will be fully paid off in three years. Beginning Balance $500,000.00 Ending Balance Payment Interest Paid Principal Paid (20 points)

Answer 1

Given, 500000 loan at a rate of 7% for 3 years.

1st we need to calculate the annual payment using formula

A = PV*i/(1 - (1+i)^(-t))

So, A = 500000*0.07/(1-1.07^(-3)) = $190525.83

Interest paid in a year = 7% of Beginning balance

So for 1st year, Interest paid = 0.07*500000 = $35000

Principal paid = Annual payment - interest paid

So, principal paid for year 1 = 190525.83-35000 = $155525.83

Ending balance = Beginning balance - Principal paid

So, Ending Balance for year 1 = 500000-155525.83 = $344474.17

using the same formula, following amortization schedule is prepared

Year	Beginning Balance	Payment	Interest Paid	Principal Paid	Ending Balance
1	$500000	$190525.83	$35000	$155525.83	$344474.17
2	$344474.17	$190525.83	$24113.19	$1666412.64	$178061.53
3	$178061.52	$190525.83	$12464.31	$178061.52	$0