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What’s the FV of an initial $100 after 3 years if i = 10%?

What’s the FV of an initial $100 after 3 years if i = 10%?. 0. 1. 2. 3. 10%. 100. FV = ?. Finding FVs (moving to the right on a time line) is called compounding. Here’s the setup to find FV:. INPUTS. N I/YR PV PMT FV. OUTPUT.

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What’s the FV of an initial $100 after 3 years if i = 10%?

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  1. What’s the FV of an initial $100 after 3 years if i = 10%? 0 1 2 3 10% 100 FV = ? Finding FVs (moving to the right on a time line) is called compounding.

  2. Here’s the setup to find FV: INPUTS N I/YR PV PMT FV OUTPUT Clearing automatically sets everything to 0, but for safety enter PMT = 0. 2nd, P/Y, 1 ENTER

  3. Calculations using Excel (in edit mode, click on the insert below for Excel)

  4. What’s the PV of $100 that will be received in 3 years if i = 10%? Finding PVs is discounting, and it’s the reverse of compounding. 0 1 2 3 10% 100 PV = ?

  5. Solve FVn = PV(1 + i )n for PV: 3 1 ö æ ÷ PV = $100 ç ø è 1.10 ( ) = $100 0.7513 = $75.13.

  6. Financial Calculator Solution INPUTS N I/YR PV PMT FV OUTPUT Either PV or FV must be negative. Here PV = -75.13. Put in $75.13 today, take out $100 after 3 years.

  7. Calculations using Excel (in edit mode, click on the insert below for Excel)

  8. Finding the Time to Double How many years will it take your $1 investment to equal $2 if the interest rate is 20 percent? … 0 1 ? FV = PV(1 + i)n $2 = $1(1 + 0.20)n

  9. Financial Calculator INPUTS N I/YR PV PMT FV OUTPUT

  10. Calculations using Excel (in edit mode, click on the insert below for Excel)

  11. What interest rate would cause $100 to grow to $125.97 in 3 years? 0 1 2 3 i% The funds grew by 25.97%. Why can’t I just divide by 3 for the yearly rate?Note 25.97% / 3 = 8.6567%.

  12. N I/YR PV FV Solution $100(1 + i )3 = $125.97. INPUTS PMT OUTPUT

  13. Calculations using Excel (in edit mode, click on the insert below for Excel)

  14. What if you were asked for a monthly rate?From the prior problem, you know the yearly rate is 8%, can you simply divide 8% by 12 to report a monthly rate of 8%/12 = 0.6667%?Let’s see…Using the same problem, but asking you to determine in months, we would state “What interest rate would cause $100 to grow to $125.97 in 36 months? Find the monthly rate.” 0 12 24 36 mo i%/mo

  15. N I/YR PV FV Solution $100(1 + i )36= $125.97. INPUTS PMT OUTPUT

  16. Calculations using Excel (in edit mode, click on the insert below for Excel)

  17. Using the monthly rate, just calculated (0.6434%), does not equal 8%/12 = 0.6667%, since dividing assumes that your money does not compound. Almost all accounts compound, so compounding should be used. A monthly rate, you are given/asked monthsA quarterly rate, you are given/asked quartersA yearly rate, you are given asked years In the next notes, we will focus on when you can divide a nominal rate (APR) and when you can’t divide, as in an effective annual rate (EAR).

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