Outstanding Loan Balance Calculation
The outstanding loan balance at any given time during the term of a loan can be calculated by finding the present value of the remaining payments at the given interest rate. This amount will consist of principal only.
Example of O/S loan balance calculation:
- Loan Amount= $100,000
- Term= 20 years
- Interest Rate = 7%
- Payment is monthly
Question: What is the loan balance at the end of year seven?
First, calculate the monthly payments by using the loan amount ($100,000) as present value, term as 240 (20 years x 12 months/year), Interest as .583333% (7%/12 months). This will give you a monthly payment of $775.30. The Present Value of an Annuity formula should be used here to solve for monthly payment.
Next, in order to find the outstanding loan balance you will need to find the present value of the remaining payments. Use the monthly payment of $775.30 as the payment function, the term will be 156 ((20-7)x12), and .583333% as the rate. This will give you an outstanding loan balance of $79,268.02. Again, the Present Value of an Annuity formula should be used.
This means that at the end of year seven the loan can be paid off in full for the amount of $79,268.02. Typically mortgage lenders will have a balloon payment clause in the contract that will charge a fee for early payment. This is because the lender will not get the same yield if loan balance is not held to maturity.
Similarly here is a table that shows both the interest and principal portions paid for the first two years.
| Period | Interest | Principal | Balance |
|---|---|---|---|
| 1 | $583.33 | $191.97 | $99,808.03 |
| 2 | $582.21 | $193.09 | $99,614.95 |
| 3 | $581.09 | $194.21 | $99,420.74 |
| 4 | $579.95 | $195.34 | $99,225.39 |
| 5 | $578.81 | $196.48 | $99,028.91 |
| 6 | $577.67 | $197.63 | $98,831.28 |
| 7 | $576.52 | $198.78 | $98,632.50 |
| 8 | $575.36 | $199.94 | $98,432.55 |
| 9 | $574.19 | $201.11 | $98,231.44 |
| 10 | $573.02 | $202.28 | $98,029.16 |
| 11 | $571.84 | $203.46 | $97,825.70 |
| 12 | $570.65 | $204.65 | $97,621.05 |
| 13 | $569.46 | $205.84 | $97,415.21 |
| 14 | $568.26 | $207.04 | $97,208.16 |
| 15 | $567.05 | $208.25 | $96,999.91 |
| 16 | $565.83 | $209.47 | $96,790.45 |
| 17 | $564.61 | $210.69 | $96,579.76 |
| 18 | $563.38 | $211.92 | $96,367.84 |
| 19 | $562.15 | $213.15 | $96,154.69 |
| 20 | $560.90 | $214.40 | $95,940.29 |
| 21 | $559.65 | $215.65 | $95,724.64 |
| 22 | $558.39 | $216.91 | $95,507.74 |
| 23 | $557.13 | $218.17 | $95,289.57 |
| 24 | $555.86 | $219.44 | $95,070.13 |
Read more about this topic: Amortization Schedule
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