At an interest rate of 6 how much will need to be invested today to have $10,000 in 5 years
DefinitionsValue of initial investmentEnter the amount of money you are investing. Show
Start YearEnter the year in which the money was first invested. End YearEnter the future year on which you want to base your calculation. Annual interest rateAnnual rate of inflationEnter a projected annual rate of inflation. The default value (2.0%) equals the mid-point of the Bank's inflation-control target range. You may change this to any rate you wish. Effect of inflation on value of initial investmentThe value of the initial investment after the effects of inflation have been calculated, but excluding interest. Total interest earnedThe total amount of interest earned, before inflation. Interest earned, after inflationThe total amount of interest earned, after the effects of inflation have been calculated. Total future valueThe total value of the investment after the effects of inflation on the principal and interest have been calculated. Target future value of investmentEnter the future amount of money you want to have. Current investment needed for future valueThis displays the amount you would have to invest to achieve your future target, taking into account the effects of inflation. You may wish to read Introduction to Interest first With Compound Interest, you work out the interest for the first period, add it to the total, and then calculate the interest for the next period, and so on ..., like this: It grows faster and faster like this: Here are the calculations for 5 Years at 10%:
Those calculations are done one step at a time:
A simple job, with lots of calculations. But there are quicker ways, using some clever mathematics. Make A FormulaLet us make a formula for the above ... just looking at the first year to begin with: $1,000.00 + ($1,000.00 × 10%) = $1,100.00 We can rearrange it like this: So, adding 10% interest is the same as multiplying by 1.10
Note: the Interest Rate was turned into a decimal by dividing by 100: 10% = 10/100 = 0.10 Read Percentages to learn more, but in practice just move the decimal point 2 places, like this: 10% → 1.0 → 0.10 Or this: 6% → 0.6 → 0.06 The result is that we can do a year in one step:
Now, here is the magic ... ... the same formula works for any year!
So it works like this: In fact we could go from the start straight to Year 5, if we multiply 5 times: $1,000 × 1.10 × 1.10 × 1.10 × 1.10 × 1.10 = $1,610.51 But it is easier to write down a series of multiplies using Exponents (or Powers) like this: This does all the calculations in the top table in one go. The FormulaWe have been using a real example, but let's be more general by using letters instead of numbers, like this: (This is the same as above, but with PV = $1,000, r = 0.10, n = 5, and FV = $1,610.51) Here is is written with "FV" first: FV = PV × (1+r)n where FV = Future Value
ExamplesHow about some examples ... ... and what if the loan was for 5 years, but the interest rate was only 6%? Here:
... and what if the loan was for 20 years at 8%? ... you work it out! Going "Backwards" to Work Out the Present ValueLet's say your goal is to have $2,000 in 5 Years. You can get 10%, so how much should you start with? In other words, you know a Future Value, and want to know a Present Value. We know that multiplying a Present Value (PV) by(1+r)n gives us the Future Value (FV), so we can go backwards by dividing, like this: So the Formula is: PV = FV(1+r)n And now we can calculate the answer: PV = $2,000(1+0.10)5 = $2,0001.61051 = $1,241.84 In other words, $1,241.84 will grow to $2,000 if you invest it at 10% for 5 years. Another Example: How much do you need to invest now, to get $10,000 in 10 years at 8% interest rate? PV = $10,000(1+0.08)10 = $10,0002.1589 = $4,631.93 So, $4,631.93 invested at 8% for 10 Years grows to $10,000 Compounding PeriodsCompound Interest is not always calculated per year, it could be per month, per day, etc. But if it is not per year it should say so! Example: you take out a $1,000 loan for 12 months and it says "1% per month", how much do you pay back? Just use the Future Value formula with "n" being the number of months: FV = PV × (1+r)n = $1,000 × (1.01)12 = $1,000 × 1.12683 = $1,126.83 to pay back And it is also possible to have yearly interest but with several compoundings within the year, which is called Periodic Compounding. Example, 6% interest with "monthly compounding" does not mean 6% per month, it means 0.5% per month (6% divided by 12 months), and is worked out like this: FV = PV × (1+r/n)n = $1,000 × (1 + 6%/12)12 = $1,000 × (1 + 0.5%)12 = $1,000 × (1.005)12 = $1,000 × 1.06168... = $1,061.68 to pay back This is equal to a 6.168% ($1,000 grew to $1,061.68) for the whole year. So be careful to understand what is meant! APRThis ad looks like 6.25%, but is really 6.335% Because it is easy for loan ads to be confusing (sometimes on purpose!), the "APR" is often used. APR means "Annual Percentage Rate": it shows how much you will actually be paying for the year (including compounding, fees, etc). Here are some examples: Example 1: "1% per month" actually works out to be 12.683% APR (if no fees). Example 2: "6% interest with monthly compounding" works out to be 6.168% APR (if no fees). If you are shopping around, ask for the APR. Break Time!So far we have looked at using (1+r)nto go from a Present Value (PV) to a Future Value (FV) and back again, plus some of the tricky things that can happen to a loan. Now is a good time to have a break before we look at two more topics:
Working Out The Interest RateYou can calculate the Interest Rate if you know a Present Value, a Future Value and how many Periods. Example: you have $1,000, and want it to grow to $2,000 in 5 Years, what interest rate do you need? The formula is: r = ( FV / PV )1/n - 1 Note: the little "1/n" is a Fractional Exponent, first calculate 1/n, then use that as the exponent on your calculator. For example 20.2 is entered as 2, "x^y", 0, ., 2, = Now we can "plug 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 need 14.87% interest rate to turn $1,000 into $2,000 in 5 years. Another Example: What interest rate do 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 PeriodsYou can calculate how many Periods if you know a Future Value, a Present Value and the Interest Rate. Example: you want to know how many periods it will take to turn $1,000 into $2,000 at 10% interest.This is the formula (note: it uses the natural logarithm function ln): n = ln(FV / PV) / ln(1 + r)
Anyway, 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 years to turn $1,000 into $2,000 at 10% interest. 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. SummaryThe basic formula for Compound Interest is: FV = PV (1+r)n Finds the Future Value, where:
And by rearranging that formula (see Compound Interest Formula Derivation) we can find any value when we know the other three: PV = FV(1+r)n Finds the Present Value when you know a Future Value, the Interest Rate and number of Periods. r = (FV/PV)(1/n) − 1 Finds the Interest Rate when you know the Present Value, Future Value and number of Periods. n = ln(FV / PV)ln(1 + r) Finds the number of Periods when you know the Present Value, Future Value and Interest Rate (note: ln is the logarithm function) AnnuitiesWe have now covered what happens to a value as time goes by ... but what if we have a series of values, like regular loan paymentsor yearly investments? That is covered in the topic of Annuities. What is the future value of $10000 on deposit for 5 years at 6% simple interest?Summary: An investment of $10000 today invested at 6% for five years at simple interest will be $13,000.
What is the total balance for simple interest on $10000 at 5% interest for 3 years?Thus, if simple interest is charged at 5% on a $10,000 loan that is taken out for three years, then the total amount of interest payable by the borrower is calculated as $10,000 x 0.05 x 3 = $1,500. Interest on this loan is payable at $500 annually, or $1,500 over the three-year loan term.
What is the future value of $1000 after 5 years at 8% per year?An investment of $1,000 made today will be worth $1,480.24 in five years at interest rate of 8% compounded semi-annually.
How long will it take to double $1000 at 6% interest?For example, if the interest rate earned is 6%, it will take 12 years (72 divided by 6) for your money to double. If you want your money to double every 8 years, you will need to earn an interest rate of 9% (72 divided by 8).
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