Find the cost of borrowing $100,000 in Example 16.1 if the interest is compounded hourly.

Example 16.1

You wish to borrow $100,000 for 10 years at 5.0 percent annual interest. What is the difference in the cost of the loan if it is compounded yearly, monthly, or daily?

Need: Cost of borrowing $100,000 for 10 years at 5.0 percent under assumptions of 10 annual payment periods, 120 monthly periods, and 3,650 daily periods.

Know–How: The formulae for compound interest from Table 16.1 is F = P(1 + r)N

Table 16.1

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Type of Interest Period Beginning of Period End of Period Future Worth, F Simple 1 P+ rP P(1 +) 2 P+ rP P(1 + ) + rP = P(1 + 2) P+ rP P(1 + 2r) + rP = P(1 + 3r) ... ... ... ... P+ rP P(1 + Nr) Compound 1 P P(1 +) P(1 +) 2 P(1 + ) P(1 + ) + rP(1 + ) P(1 + n2 P(1 + n2 P(1 + n? + rP(1 + n? P(1 + n3 ... ... N-1 N P(1 + n P(1 + N-1 + rP(1+ nN1 P(1 + r)N