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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 Fn = 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 Fn = 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.
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