In: Finance
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)
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