Time Value of Money and Fair Value Accounting. Dr Jae K. Shim

The number of years it will take for equal periodic deposits to reach a certain future sum can be computed as follows:

      Solving for T₂, we obtain:

      where F_n = future value in period n, and P = a present sum of money or base-period value.

       Example 25

      You want $500,000 in the future. The interest rate is 10 percent. You can deposit $80,000 each year. The number of years it will take to accomplish this objective is computed below:

      From Table 2, we see that n is approximately 5 years.

Can a Computer Help?

      More exact answers can be obtained using computer software. For example, Excel has a routine NPER(rate,pmt,pv,fv,type), which calculates the number of periods for an investment based on periodic, constant payments and a constant interest rate. Furthermore, many financial calculators contain preprogrammed formulas and perform many present-value and future-value applications.

Computing Interest Rate

      You might want to know about the interest rate you are charged on a loan or the interest rate you must earn on your annual deposits to reach your investment goal.

      Case 1: Single-Deposit Loan. The interest rate you are charged on a loan can be computed as follows:

      Solving for T₁ we obtain

      where F_n = future value in period n, and P = a present sum of money or base-period value.

       Example 26

      You agree to pay back $3,000 in 6 years on a $2,000 loan made today. You are being charged an interest rate of 7 percent, calculated as follows:

      From Table 1 in the Appendix, a T₁ of 1.5 at 6 years is at 7 percent.

      Case 2: Equal Periodic Deposits. The interest rate you must earn on your annual deposits to reach your investment goal can be computed as follows:

      Solving for T₂(i,n), we obtain

      where F_n = future value in period n, and P = a present sum of money or base-period value.

       Example 27

      You want to have $500,000 accumulated in a pension plan after 9 years. You deposit $30,000 per year. The interest rate you must earn is computed below.

      From Table 2, the interest rate is approximately 15 percent.