A 10-year amortized loan of $100,000 with 5% APR requires yearly loan payment. After making four...

A 10-year amortized loan of $100,000 with 5% APR requires yearly loan payment. After making four yearly payments, the fourth year's ending loan balance is $Answer (don't include thousand separator( , ), rounding the number with two decimal places)

Expert Solution

First we need to calculate the annual payment of the loan

We are given the following information:

Payment	PMT	To be calculated
Rate of interest	r	5.00%
Number of years	n	10.00
Annual	frequency	1.00
Loan amount	PV	100000.00

We need to solve the following equation to arrive at the required PMT:

So the annual payment is 12950.46

Below is the amortization schedule:

Year	Opening Balance	PMT	Interest	Principal repayment	Closing Balance
1	$ 1,00,000.00	$ 12,950.46	$ 5,000.00	$ 7,950.46	$ 92,049.54
2	$ 92,049.54	$ 12,950.46	$ 4,602.48	$ 8,347.98	$ 83,701.56
3	$ 83,701.56	$ 12,950.46	$ 4,185.08	$ 8,765.38	$ 74,936.18
4	$ 74,936.18	$ 12,950.46	$ 3,746.81	$ 9,203.65	$ 65,732.53
5	$ 65,732.53	$ 12,950.46	$ 3,286.63	$ 9,663.83	$ 56,068.70
6	$ 56,068.70	$ 12,950.46	$ 2,803.44	$ 10,147.02	$ 45,921.68
7	$ 45,921.68	$ 12,950.46	$ 2,296.08	$ 10,654.37	$ 35,267.31
8	$ 35,267.31	$ 12,950.46	$ 1,763.37	$ 11,187.09	$ 24,080.22
9	$ 24,080.22	$ 12,950.46	$ 1,204.01	$ 11,746.45	$ 12,333.77
10	$ 12,333.77	$ 12,950.46	$ 616.69	$ 12,333.77	$ 0.00
		$ 1,29,504.57	$ 29,504.57	$ 1,00,000.00

Opening balance = previous year's closing balance
Closing balance = Opening balance+Loan-Principal repayment
PMT is calculated as per the above formula
Interest = 0.05 x opening balance
Principal repayment = PMT - Interest
So after the payment at the end of year 4, the loan balance is $65,732.53

jeff jeffy answered 2 years ago

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