Question

In: Finance

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)

Solutions

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


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