While talking with a financial advisor, she insisted that a regular person could not calculate things like future value without a spreadsheet designed by the bank's actuary. While that's true for complex insurance estimations and market forecasts, basic calculations in personal finance rarely require more than high school math. Unfortunately, in today's computer age, people are used to online calculators, spreadsheet, etc... and such basic math skills are largely overlooked. Let's talk about some of the most common calculation done in personal finance.
1. compound growth
We all know the power of compound interest and time. For example, a $10,000 investment grow at 10% annual return over 40 years might sound like it can grow to $50,000. In reality, it would actually grow to $$452,592.56
Let's assume our principle is X, and our annual return rate is r
After 1 year, we would have X * (1+r)
After 2 years, we would have X * (1+r) * (1+r)
After 3 years, we would have X * (1+r) * (1+r) * (1+r)
We can already see the pattern here. Therefore,
After n years, we would have X * (1+r)^n
Going back to our example, $10,000 investment grow at 10% annually over 40 years would be worth
$10,000 * (1+10%)^40 = $452,592.56
It's interesting to note that the original investment is actually the least important variable in the equation since it's a linear component. For example, half the investment will result in exactly half the future value.
$5,000 * (1+10%)^40 = $226,296.28
The interest rate and time, on the other hand, can causes much bigger changes. For example, half the interest rate would lower the future value to only about 7 times.
$10,000 * (1+5%)^40 = $70,399.89
Similarly, half the investment time would lower the future value even more
$10,000 * (1+10%)^20 = $67,275.00
1. compound growth
We all know the power of compound interest and time. For example, a $10,000 investment grow at 10% annual return over 40 years might sound like it can grow to $50,000. In reality, it would actually grow to $$452,592.56
Let's assume our principle is X, and our annual return rate is r
After 1 year, we would have X * (1+r)
After 2 years, we would have X * (1+r) * (1+r)
After 3 years, we would have X * (1+r) * (1+r) * (1+r)
We can already see the pattern here. Therefore,
After n years, we would have X * (1+r)^n
Going back to our example, $10,000 investment grow at 10% annually over 40 years would be worth
$10,000 * (1+10%)^40 = $452,592.56
It's interesting to note that the original investment is actually the least important variable in the equation since it's a linear component. For example, half the investment will result in exactly half the future value.
$5,000 * (1+10%)^40 = $226,296.28
The interest rate and time, on the other hand, can causes much bigger changes. For example, half the interest rate would lower the future value to only about 7 times.
$10,000 * (1+5%)^40 = $70,399.89
Similarly, half the investment time would lower the future value even more
$10,000 * (1+10%)^20 = $67,275.00