1. Describe the process for solving for the interest rate in present and future
ID: 2691060 • Letter: 1
Question
1. Describe the process for solving for the interest rate in present and future value problems. 2. Describe the process for solving for the time period in present and future value problems.Explanation / Answer
Solve Problems Related to Present Value (PV) and Future Value (FV) Present Value (PV) Let’s suppose you want to determine the current value of the ultimate earnings on an investment. This question could be restated in the following manner: What is the present value of my investment that will mature in n years at i percent interest (or discount rate)? To solve this problem, you will need to know the future value of your investment, how many years are required for the investment to reach maturity, and what interest or discount rate your investment has. The result of the equation will be a dollar amount that is smaller than the future amount of principal and interest that you will have earned; it is the amount that the investment is worth at the present time. The present value (PV) equation is as follows: PV = future value/ (1 + interest rate)n In this equation, n is the number of periods (years in this case). The key inputs in the PV equation are as follows: FV = the future value of the investment at the end of n years N = the number of years in the future I = the interest rate, or the annual interest rate or discount rate PV = the present value, in today’s dollars, of a sum of money that you have invested or plan to invest After you find these inputs, you can solve for the present value (PV). You must remember that money you will earn in the future is less valuable than money you have right now; this is because you cannot use future money to earn interest today. You can only earn interest with money you have in hand. 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: Iteration - by calculating the future value for different values of interest rate or time, one gradually can converge on the solution. Financial calculator or spreadsheet - use built-in functions to instantly calculate the solution. 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. 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 Finance > Future Value Home | About | Privacy | Reprints | Terms of Use Copyright © 2002-2010 NetMBA.com. 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