Overview of Loan Outstanding Balance Calculation
This lesson focuses on calculating the outstanding balance of a loan using the Present Value (PV) method. It highlights the difference between the Present Value and Future Value methods and emphasizes that this guide is specific to the PV approach.
Key Concepts
- Loan Amount: The principal amount borrowed (e.g., 100,000 Rand).
- Interest Rate: Annual interest rate converted to a monthly rate (16% annually = 0.016/12 monthly).
- Loan Term: Total repayment period in months (5 years × 12 = 60 months).
- Monthly Payment: The fixed amount paid monthly to repay the loan.
Step 1: Calculate the Monthly Payment
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Use the Present Value formula for an annuity: [ PV = PMT \times \frac{1 - (1 + i)^{-n}}{i} ] where:
- PV = loan amount (100,000 Rand)
- PMT = monthly payment (unknown)
- i = monthly interest rate (0.016/12)
- n = total number of payments (60)
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Rearrange the formula to solve for PMT.
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Avoid rounding intermediate calculations to maintain accuracy.
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Using a financial calculator or spreadsheet, the monthly payment is approximately 2,431.81 Rand.
Step 2: Calculate the Outstanding Balance After 2 Years
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The outstanding balance is the present value of the remaining payments.
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After 2 years (24 payments), the remaining term is 3 years (36 payments).
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Use the Present Value formula again with:
- PMT = 2,431.81 Rand
- i = 0.016/12
- n = 36 (remaining payments)
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The outstanding balance is approximately 69,169.94 Rand.
Important Notes
- The number of payments (n) in the outstanding balance formula refers to the remaining payments, not the payments already made.
- The Present Value method calculates how much the borrower still owes at a given point in time.
- Some students prefer the Future Value method, but this lesson focuses solely on the Present Value approach.
Summary
By applying the Present Value method, you can accurately determine both the monthly payment required to repay a loan and the outstanding balance after a certain period. This method is essential for understanding loan amortization and managing repayments effectively.
For further reading on related financial concepts, check out our guides on Understanding Bank Balance Sheets: A Comprehensive Guide to T-Accounts and Comprehensive Overview of Financial Management and Capital Budgeting Techniques. Additionally, if you're interested in the mathematical principles behind these calculations, you may find Understanding Averages, Ratios, and Proportions in Mathematics helpful.
in this lesson we are going to be looking at how to calculate the outstanding balance but I would like to
mention that we're going to be using the Present Value method remember there are two ways to do outstanding balance you
can use the Present Value method or the Future Value method if you do not use the Present Value method then rather
skip this video and look at my video on future value in this question we have a person who takes out a loan that needs
to be repaid in 5 years and they give us the interest rate everything looks looks good it's easy they're not they're not
making late payments or anything like that so we so question a says determine the monthly payment so this is very
straightforward we know that this person wants 100,000 Rand and it's a loan guys do when you take out a loan you don't
get the money in the future you get the money on the day that you take out the loan that is called the present this is
why we're using the present value formula so we can say 100,000 equals to the monthly payment which we don't know
the interest rate is 16% which I like to say 016 over 12 and then the number of
payments will just be 5 * 12 which is 60 now there are multiple ways to get X alone over here one way and and as as I
said there are so many ways you could just type all of this on your calculator some students like to take the Z the
this part over here they take it up I actually do it that way but for some reason I just feel like doing it like
this in this lesson now you don't want to round off when you do this method so we'll say 100,000 to
41121 7062 X then you can get X alone on the CIO calculators you could just say 100,000 / answer which will be your
previous answer and we should get an answer of 2,431 r81 cents if we round to two
decimal places now we are going to work out the balance outstanding now if you use the Present Value method you
literally just use the present value form fora and your n value will be the number
of payments that you still need to make guys that is important that you hear what I just said it is the number of
payments that you still need to make not the number of payments that have already happened it's the number of payments
that you still need to make okay so what we do is we go say p equals to now we can use our monthly payment that we've
calculated in the previous question and then the interest rate is 16% that all stays the same now it's a 5-year
question but they want to know what is the balance outstanding after 2 years so guys how many years do we still have
well we still have another 3 years and so 3 * 12 is 36 and that's it the Present Value method for outstanding
balance is quite an easy one but some students do prefer the Future Value method all right and what this tells
this is that the present value is going to be 69,1 16994 and that would be in Rand so what
that technically means is that that's how much money this person still owes on their loan that is how much they still
need to pay to the bank
Heads up!
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