Future values
This presentation is the property of its rightful owner.
Sponsored Links
1 / 18

Future Values PowerPoint PPT Presentation


  • 48 Views
  • Uploaded on
  • Presentation posted in: General

Future Values. Suppose you invest $1000 for one year at 5% per year. What is the future value in one year? Interest = 1000(.05) = 50 Value in one year = principal + interest = 1000 + 50 = 1050 Future Value (FV) = 1000(1 + .05) = 1050

Download Presentation

Future Values

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Future values

Future Values

  • Suppose you invest $1000 for one year at 5% per year. What is the future value in one year?

    • Interest = 1000(.05) = 50

    • Value in one year = principal + interest = 1000 + 50 = 1050

    • Future Value (FV) = 1000(1 + .05) = 1050

  • Suppose you leave the money in for another year. How much will you have two years from now?

    • FV = 1000(1.05)(1.05) = 1000(1.05)2 = 1102.50


Effects of compounding

Effects of Compounding

  • Simple interest

  • Compound interest

  • Consider the previous example

    • FV with simple interest = 1000 + 50 + 50 = 1100

    • FV with compound interest = 1102.50

    • The extra 2.50 comes from the interest of .05(50) = 2.50 earned on the first interest payment


Future values example 3

Future Values – Example 3

  • Suppose you had a relative deposit $10 at 5.5% interest 200 years ago. How much would the investment be worth today?

    • FV = 10(1.055)200 = 447,189.84

  • What is the effect of compounding?

    • Simple interest = 10 + 200(10)(.055) = 210.55

    • Compounding added $446,979.29 to the value of the investment


Present values

Present Values

  • How much do I have to invest today to have some amount in the future?

    • FV = PV(1 + r)t

    • Rearrange to solve for PV = FV / (1 + r)t

  • There are four parts to this equation

    • PV, FV, r and t

    • If we know any three, we can solve for the fourth

  • When we talk about discounting, we mean finding the present value of some future amount.


Pv one period example

PV – One Period Example

  • Suppose you need $10,000 in one year for the down payment on a new car. If you can earn 7% annually, how much do you need to invest today?

  • PV = 10,000 / (1.07)1 = 9345.79

  • Calculator

    • 1 N

    • 7 I/Y

    • 10,000 FV

    • PV = -9345.79


Present values example 1

Present Values – Example 1

  • You want to begin saving for you daughter’s college education and you estimate that she will need $150,000 in 17 years. If you feel confident that you can earn 8% per year, how much do you need to invest today?

    • PV = 150,000 / (1.08)17 = 40,540.34

    • Calculator

      • 17 N

      • 8 I/Y

      • 150,000 FV

      • PV

      • -40,540.34


Present values example 2

Present Values – Example 2

  • Your parents set up a trust fund for you 10 years ago that is now worth $19,671.51. If the fund earned 7% per year, how much did your parents invest?

    • PV = 19,671.51 / (1.07)10 = 10,000

      Financial Calculator

    • 19,671.51 FV

    • 7 I/YR

    • 10 N

    • PV


Discount rate example 1

Discount Rate – Example 1

  • You are looking at an investment that will pay $1200 in 5 years if you invest $1000 today. What is the implied rate of interest?

    • r = (1200 / 1000)1/5 – 1 = .03714 = 3.714%

    • Calculator – the sign convention matters!!!

      • 5 N

      • 1000 +/- PV (you pay 1000 today)

      • 1200 FV (you receive 1200 in 5 years)

      • I/Y

      • Answer 3.714%


Discount rate example 2

Discount Rate – Example 2

  • Suppose you are offered an investment that will allow you to double your money in 6 years. You have $10,000 to invest. What is the implied rate of interest?

    • r = (20,000 / 10,000)1/6 – 1 = .122462 = 12.25%

    • Calculator

      • 6 N

      • 1000 +/- PV

      • 20,000 FV

      • I/Y


Discount rate example 3

Discount Rate – Example 3

  • Suppose you have a 1-year old son and you want to provide $75,000 in 17 years towards his college education. You currently have $5000 to invest. What interest rate must you earn to have the $75,000 when you need it?

    • r = (75,000 / 5,000)1/17 – 1 = .172688 = 17.27%

    • Calculator

      • 17 N

      • 5,000 +/- PV

      • 75,000 FV

      • I/Y


Number of periods example 1

Number of Periods – Example 1

  • You want to purchase a new car and you are willing to pay $20,000. If you can invest at 10% per year and you currently have $15,000, how long will it be before you have enough money to pay cash for the car?

    • t = ln(20,000 / 15,000) / ln(1.1) = 3.02 years

    • Calculator

      • 10 I/Y

      • 15,000 +/- PV

      • 20,000 FV

      • N


Multiple cash flows fv example 1

Multiple Cash Flows – FV Example 1

  • Suppose you invest $500 in a mutual fund today and $600 in one year. If the fund pays 9% annually, how much will you have in two years?

    • FV = 500(1.09)2 + 600(1.09) = 1248.05

  • How much will you have in 5 years if you make no further deposits?

  • First way:

    • FV = 500(1.09)5 + 600(1.09)4 = 1616.26

  • Second way – use value at year 2:

    • FV = 1248.05(1.09)3 = 1616.26


Multiple cash flows pv another example

Multiple Cash Flows – PV Another Example

  • You are considering an investment that will pay you $1000 in one year, $2000 in two years and $3000 in three years. If you want to earn 10% on your money, how much would you be willing to pay?

    • PV = 1000 / (1.1)1 = 909.09

    • PV = 2000 / (1.1)2 = 1652.89

    • PV = 3000 / (1.1)3 = 2253.94

    • PV = 909.09 + 1652.89 + 2253.94 = 4815.93


Annuity sweepstakes example

Annuity – Sweepstakes Example

  • Suppose you win the Publishers Clearinghouse $10 million sweepstakes. The money is paid in equal annual installments of $333,333.33 over 30 years. If the appropriate discount rate is 5%, how much is the sweepstakes actually worth today?

    • PV = 333,333.33[1 – 1/1.0530] / .05 = 5,124,150.29

      Financial Calculator

      333,333.33 PMT; 5 I/YR; 30 N; PV


Finding the payment

Finding the Payment

  • Suppose you want to borrow $20,000 for a new car. You can borrow at 8% per year, compounded monthly (8/12 = .66667% per month). If you take a 4 year loan, what is your monthly payment?

    • 20,000 = C[1 – 1 / 1.006666748] / .0066667

    • C = 488.26

      Financial Calculator

    • 20,000 PV; 48 N; .6666 I/YR; PMT


Finding the number of payments another example

Finding the Number of Payments – Another Example

  • Suppose you borrow $2000 at 5% and you are going to make annual payments of $734.42. How long before you pay off the loan?

    • 2000 = 734.42(1 – 1/1.05t) / .05

    • .136161869 = 1 – 1/1.05t

    • 1/1.05t = .863838131

    • 1.157624287 = 1.05t

    • t = ln(1.157624287) / ln(1.05) = 3 years

      Financial Calculator

      $2000 PV; 734.42 +/- PMT; 5 I/YR; N


Finding the rate

Finding the Rate

  • Suppose you borrow $10,000 from your parents to buy a car. You agree to pay $207.58 per month for 60 months. What is the monthly interest rate?

    • Sign convention matters!!!

    • 60 N

    • 10,000 PV

    • -207.58 PMT

    • I/Y = .75%


Future values for annuities

Future Values for Annuities

  • Suppose you begin saving for your retirement by depositing $2000 per year in an IRA. If the interest rate is 7.5%, how much will you have in 40 years?

    • FV = 2000(1.07540 – 1)/.075 = 454,513.04

      Financial Calculator

    • -2000 PMT (use +/- key to change sign)

    • 40 N

    • 7.5 I/YR

    • FV = $454,513.03


  • Login