High School Finance Curriculum (1)

High School Finance Curriculum--Double an Investment

A recent article posted on Reddit.com got my attention. It was about Oklahoma schools being required to teach high school students how to manage their finances. I think it’s important for students to understand accounting, banking, and business.

To keep refreshed on business topics covered by such a curriculum requirement, I’m posting some information based on these topics.

The first topic—how long is needed to double an investment by using an exact calculation and by estimating with Rule 72.

Example 1. About how many years would it take for $1,000 to become $2,000 if $1,000 is deposited in a savings account with an interest rate of 7.2 percent?

Using Rule of 72 (or 70)

To estimate the number of periods required to double an original investment, divide the most convenient "rule-quantity" by the expected growth rate, expressed as a percentage.

72/7.2 = 10 years

Using Exact Calculation

For periodic compounding, the exact doubling time for an interest rate of r per period is:

T = ln(2)/ln(1+r)

T = ln(2)/ln(1.072)

T = .69315/.06953

T = 9.96904 or about 10 years

Example 2. How long would it take to double an initial investment of $100 with compounding interest at a rate of 9% per annum.

The rule of 72 gives 72/9 = 8 years required for the investment to be worth $200.

An exact calculation gives ln(2)/ln(1+.09) = 8.0432 years.