Jun 12, 2010

MBA Finance Topics-FUTURE VALUE

How to calculate the future value of a present sum of money.

The future value of a sum of money invested at interest rate i for one year is given by:

FV = PV ( 1 + i )

where

FV = future value
PV = present value
i = annual interest rate

If the resulting principal and interest are re-invested a second year at the same interest rate, the future value is given by:

FV = PV ( 1 + i ) ( 1 + i )

In general, the future value of a sum of money invested for t years with the interest credited and re-invested at the end of each year is:

FV = PV ( 1 + i ) t

Solving for Required Interest Rate or Time

Given a present sum of money and a desired future value, one can determine either the interest rate required to attain the future value given the time span, or the time required to reach the future value at a given interest rate. Because solving for the interest rate or time is slightly more difficult than solving for future value, there are a few methods for arriving at a solution:

1.

Iteration - by calculating the future value for different values of interest rate or time, one gradually can converge on the solution.
2.

Financial calculator or spreadsheet - use built-in functions to instantly calculate the solution.
3.

Interest rate table - by using a table such as the one at the end of this page, one quickly can find a value of interest rate or time that is close to the solution.
4.

Algebraic solution - mathematically calculating the exact solution.

Algebraic Solution

Beginning with the future value equation and given a fixed time period, one can solve for the required interest rate as follows.

FV = PV ( 1 + i ) t

Dividing each side by PV and raising each side to the power of 1/t:

( FV / PV ) 1/t = 1 + i

The required interest rate then is given by:

i = ( FV / PV ) 1/t - 1

To solve for the required time to reach a future value at a specified interest rate, again start with the equation for future value:

FV = PV ( 1 + i ) t

Taking the logarithm (natural log or common log) of each side:

log FV = log [ PV ( 1 + i ) t ]

Relying on the properties of logarithms, the expression can be rearranged as follows:

log FV = log PV + t log ( 1 + i )

Solving for t:

t =


log ( FV / PV )

log ( 1 + i )

Interest Factor Table

The term ( 1 + i ) t is the future value interest factor and may be calculated for an array of time periods and interest rates to construct a table as shown below:

Table of Future Value Interest Factors

t \ i
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
1
1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090 1.100
2
1.020 1.040 1.061 1.082 1.103 1.124 1.145 1.166 1.188 1.210
3
1.030 1.061 1.093 1.125 1.158 1.191 1.225 1.260 1.295 1.331
4
1.041 1.082 1.126 1.170 1.216 1.262 1.311 1.360 1.412 1.464
5
1.051 1.104 1.159 1.217 1.276 1.338 1.403 1.469 1.539 1.611
6
1.062 1.126 1.194 1.265 1.340 1.419 1.501 1.587 1.677 1.772
7
1.072 1.149 1.230 1.316 1.407 1.504 1.606 1.714 1.828 1.949
8
1.083 1.172 1.267 1.369 1.477 1.594 1.718 1.851 1.993 2.144
9
1.094 1.195 1.305 1.423 1.551 1.689 1.838 1.999 2.172 2.358
10
1.105 1.219 1.344 1.480 1.629 1.791 1.967 2.159 2.367 2.594
11
1.116 1.243 1.384 1.539 1.710 1.898 2.105 2.332 2.580 2.853
12
1.127 1.268 1.426 1.601 1.796 2.012 2.252 2.518 2.813 3.138
13
1.138 1.294 1.469 1.665 1.886 2.133 2.410 2.720 3.066 3.452
14
1.149 1.319 1.513 1.732 1.980 2.261 2.579 2.937 3.342 3.797
15
1.161 1.346 1.558 1.801 2.079 2.397 2.759 3.172 3.642 4.177
Source: www.netmba.com

No comments:

Post a Comment

Tags

accredited distance education Ambush Marketing Benchmarking Benefits of MBA Books Branding Business Communication Business Negotiation Career Guide Case Studies CMAT Consumer Adoption Process Corporate Social Responsibility CRM CV Writing Debentures Depreciation Distance Learning Economics topics EMBA Entrepreneurship Finance your MBA Financial Analysis Financial Management Financial Planning Financial statement Formal Report Fund Flow Statement Gmat GRI Group Discussion Hotel Management HR notes International Marketing Leadership Letter of Intent london business school Management Notes Manager of Sales Managerial Decisions Marketing Concepts Marketing Management Marketing Mix Marketing Tips MBA Assignment MBA Careers mba courses MBA Definitions mba degree MBA Dissertation Topics MBA Economics Project MBA Finance Topics MBA Glossary MBA Guide MBA in Australia mba in canada MBA in International Business MBA in IT mba in malaysia MBA in public relations MBA in UK mba in usa MBA Interview MBA Jobs MBA Jobs In Australia MBA Loan MBA Notes MBA Outsourcing MBA Presentations MBA Prjoject Reports MBA Programs MBA Ranking MBA Salary MBA Scholarships MBA Sponsorships MBA Student MBA without GMAT MBO Media Planning Process Mini MBA Motivation Online Accredited MBA online mba Online MBA and Correspondence MBA Opportunity Cost Overseas Education Consultants Part Time MBA PEST analysis PLC Popular Business Schools Porter's 5 Forces Profit Maximization and Wealth Maximization Project Management Project Report Projects Tips Resume Writing Scientific Management Segmentation Strategic management Study Abroad Study in Germany Supply Chain Management SWOT Team Management Skills Theories top mba TQM Trade Discounts Training & Development Trend Analysis Types Of MBA Views of Management viral marketing Women In MBA