With that we can work out FV when we know PV, the Interest Rate and Number of Periods But by rearranging that formula we can find FV, the Interest Rate or the Number of Periods when we know the other three, like this:
How did we get those other three formulas? Read On! Working Out the Present ValueLet's say you want to reach $2,000 in 5 Years at 10%. How much should you start with? In other words, you know a Future Value, and want to know a Present Value. We can just rearrange the formula to suit ... dividing both sides by (1+r)^{n} to give us: So now we can calculate the answer: PV = $2,000 / (1+0.10)^{5} = $2,000 / 1.61051 = $1,241.84 It works like this: Another Example: How much would you need to invest now, to get $10,000 in 10 years at 8% interest rate? PV = $10,000 / (1+0.08)^{10} = $10,000 / 2.1589 = $4,631.93 So, $4,631.93 invested at 8% for 10 Years would grow to $10,000 Working Out The Interest RateIf you have $1,000, and want it to grow to $2,000 in 5 Years, what interest rate do you need? We need a rearrangement of the first formula to work it out. Now we have the formula, it is just a matter of "plugging in" the values to get the result: r = ( $2,000 / $1,000 )^{1/5} - 1 = ( 2 )^{0.2} - 1 = 1.1487 - 1 = 0.1487 And 0.1487 as a percentage is 14.87%, So you would need a 14.87% interest rate to turn $1,000 into $2,000 in 5 years. Another Example: What interest rate would you need to turn $1,000 into $5,000 in 20 Years? r = ( $5,000 / $1,000 )^{1/20} - 1 = ( 5 )^{0.05} - 1 = 1.0838 - 1 = 0.0838 And 0.0838 as a percentage is 8.38%. So 8.38% will turn $1,000 into $5,000 in 20 Years. Working Out How Many PeriodsIf you want to know how many periods it will take to turn $1,000 into $2,000 at 10% interest, you can also rearrange the basic formula. But we need to use the natural logarithm function ln() to do it. Now let's "plug in" the values: n = ln( $2,000 / $1,000 ) / ln( 1 + 0.10 ) = ln(2)/ln(1.10) = 0.69315/0.09531 = 7.27 Magic! It will need 7.27 periods to turn $1,000 into $2,000 at 10% interest. Another Example: How many years to turn $1,000 into $10,000 at 5% interest? n = ln( $10,000 / $1,000 ) / ln( 1 + 0.05 ) = ln(10)/ln(1.05) = 2.3026/0.04879 = 47.19 47 Years! But we are talking about a 10-fold increase, at only 5% interest. ConclusionNow that you see how each formula was derived and how to use it, hopefully it will be easier for you to remember them, and to be able to use them in different situations. |