In 1995, O. G. McClain of Houston, Texas, mailed a 00 check to a descendant of Texas independenc

step 1 to find the interest rate pay annum if we are given that the principal loan was $100 and the acc

In 1995, O. G. McClain of Houston, Texas, mailed a 00 check...

In $1995,$ O. G. McClain of Houston, Texas, mailed a \$100 check to a descendant of Texas independence hero Sam Houston to repay a \$100 debt of McClain's great-great-grandfa- ther, who died in 1835 , to Sam Houston. A bank estimated the interest on the loan to be $\$ 420$ million for the 160 years it was due. Find the interest rate the bank was using, assuming interest is compounded annually. Source: The New York Times.

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Key Concepts

Time Value of Money

The time value of money is the idea that a sum of money has a different value today than it will at some point in the future, due to its potential earning capacity. This concept takes into account factors like interest rates and compounding frequency, illustrating how even small amounts can grow significantly over extended periods.

Compound Interest

Compound interest is a fundamental financial concept where interest is calculated on the initial principal and also on the accumulated interest from previous periods. This results in an exponential growth of the investment or debt over time, as each period’s interest is calculated on an increasingly larger base. It is central to understanding how quickly debts can grow and how investments can multiply over long periods.

Solving Exponential Equations Using Logarithms

When dealing with compound interest formulas that involve exponential growth over time, it is often necessary to solve for variables in the exponent, such as the interest rate. This is typically done using logarithms, which allow one to 'bring down' the exponent and solve for the unknown, a crucial step in many financial calculations involving long-term growth or decay.

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