Category Archives: Math to Make Money

How Portfolio Weighted Returns are Calculated

One of the reasons why we pay financial advisers and analysts to handle our investment accounts is because they are better able to deal with the confusing mathematics associated with the returns of an overall portfolio.

African american lifting weightsHowever, if we ignore the complicated statistics of correlations, related exposures, and other advanced statistical metrics, we can start to take control of our own personal investment portfolios by understanding how it is that the returns of the full collection of securities are calculated. By being aware of how it is that these weighted averages will build up the actual returns that we see in our bank accounts, we can then begin to look at how it is that taking on different amounts of risk will pay off or punish us in the future.

The first step to calculating our portfolio returns is to total up the value of all the money in our accounts. For now, let’s assume that our total portfolio value is $10,000. From there, we divide out the dollar value of each investment in the portfolio by the total amount, to find out how much of our portfolios is made up by that one investment.

If we have a portfolio of 4 investments worth $2,500 each, we therefore have an individual weighting of 25% for each security. The last step is to then multiply out the yield returns of these securities by their individual weightings, and to add them up. This will present us with the expected return of each security in the portfolio, after taking into consideration the fact that each of the different securities will be producing different amounts of returns. The table below illustrates our example: Continue reading

The Rule of 72 for Quick Estimations

One of the more popular financial tricks in personal finance is referred to as the Rule of 72. Acting as a tool for quick estimations, the equation states that dividing the number 72 by the interest rate of an investment will show you how many years it takes to double your money in a given investment. As such, an investment into a savings account that pays 3% interest will double its principle amount in 24 years. Comparatively, an investment in a bond that pays 5% will double in 14.5 years. With that in mind, we can look at how it is that this rule can be taken a step further to evaluate our future wealth goals.

Nr. 72The first way to look at the ability of the rule of 72 to help us understand our ability to meet our long term financial goals is in terms of its applications in a portfolio. While we might have a bond that will double in 14.5 years, a portion of our money will still be in that savings account at 3% that will take 24 years to double.

If we have equal amounts of money in either of these products, we need to look at the average term values of these investments, and re-evaluate to determine how long it will take for the portfolio as a whole to double. We therefore need to divide each of these values by 2 (because they both make up half of our portfolio), and add them together. Continue reading

Credit Card Calculations Including Interest and Payments

Credit cards are by far one of the more complicated financial innovations in terms of personal finance. Ignoring the complexities of cash back and rewards points, as well as the benefits of a grace period on the first month’s interest, the way in which credit cards compound interest is slightly different than the way in which a normal loan or revolving line of credit would operate.

credit-cardsAs such, the equation for calculating how much time you have left on your credit card at a certain payment amount is a fairly complex beast. That being said, the underlying assumptions of the equation should be enough on its own to motivate us towards doing the math, and finding out how to get rid of these balances as soon as possible.

Credit cards differ from personal loans because of the way in which they compound interest on top of the full monthly balance that was carried, even if a payment has been made on the loan amount. This means that the amount of interest that we are paying on a credit card will always be higher than on even a comparable revolving line of credit. The addition of interest upon payments also results in a somewhat different payment schedule for the loan, as well as a period of latency between when we think we’ve paid off a card, and when we have actually paid off the card. Continue reading

Understanding Loan Calculations

Having looked at how present value and future value equations can help us to understand what our payment schedules look like in terms of their true values, we can now start to dive into the equations that bankers use to determine how much our monthly payments on various types of loans will be. From there, we can apply that amount to our debt-servicing ratio to see just how much capacity for debt we have as a borrower.

loan-calculationsThe loan payment equation comes off as being particularly complicated, but it’s actually quite simple when we look at it conceptually. We are simply determining the optimized rate of the declining balance, and then assigning that percentage a dollar value. In symbolic terms, it works out to the following:

Payment=Principle*Interest RatePayment Periods1-(1+Interest RatePayment Periods) –Payment Continue reading

Understanding and Using Future Values

In the previous article we discussed how it is that we can use the present value function to understand what a set payment schedule is worth to us in terms of dollars today. While present value is very useful for us to compare different investment opportunities in terms of their worth to us today, the future value equation helps us to evaluate the true costs of our debts and obligations, by showing us exactly how much will be paid out in total over the course of the same payment schedule.

E-moneyThe future value equation is similar to the present value function, in that it requires the same information to calculate (payment amount, number of payment periods, and interest rate). That being said, the future value equation differs slightly in the way that it is calculated.

Future Value=Payments (1+Interest Rate) #PeriodsInterest Rate-1Interest Rate

Looking again at our bond that pays out $200 semi-annually for 5 years in an environment where a savings account pays out 3%/year, which we will remember had a present value of $1844.44, we can see that the equation is calculated as follows: Continue reading

Understanding and Using Present Values

One of the most valuable additions to a savers toolkit is the present value calculation. Even though it comes off as a bit scary at first, the amount of value it creates as a tool for understanding our financial position by putting the numbers right in front of us. By using the present value function, we can then start to look at how it is that our future obligations and investments impact us today.

equationsThe present value equation looks at money that we will be receiving at a later date, and tells us how much that amount of money is worth to us today. From there, we can compare the different aspects of our financial position to find out which obligation should take on a higher priority to pay off first, or which investment is worth more to us in the longer term.

To calculate the present value of a payment schedule, we need to know the number of payments that will be made/received, the number of periods in which we will receive these payments, and the interest rate under which these payments will be operating. From there, we multiply the dollar value of the payments by the inverse of the interest rate, less the interest rate multiplied by its full percentage amount, to the power of the number of periods in which we will receive/pay those payments. Don’t let the verbal explanation confuse you, it’s much simpler when you see it symbolically: Continue reading

Understanding Compound Interest

Keeping track of personal finances can be a somewhat daunting task for anyone. Between the hassle associated with rounding up all of the proper documents, the potential for disappointment when we see that we might be behind our financial goals, and the sheer amount of time that we need to spend making sure that we are setting ourselves back on track, it’s fairly easy to find an excuse to procrastinate this task off to another day.

compound interest equationHowever, financial planning doesn’t need to be a chore, and can actually be a fairly seamless process for an informed saver. The trick is to understand the financial math that goes into our daily lives, so that we can better see how our money is working in our daily lives, and what we need to do to make our savings work for us.

The most fundamental calculation for a personal saver to understand is the compounding interest equation. Compounding interest, as a concept, makes up the basis of any kind of banking, and is therefore has an impact on our savings, borrowing, and investing. Simply put, compounding interest represents the way in which an interest rate is broken down to accumulate on a daily basis, so as to be most efficient.

When interest compounds it will result in a higher interest amount being paid (or received), but also represent a much more efficient amount than simple interest (which is just paid off at the end of the period). From a debt perspective, we will see later on how it is that compounding interest is the reason why a debt is so cumbersome in the first half of a loan period, while it creates a much more appealing return from an investment and savings perspective. Continue reading