Investments increase exponentially by about $26 \%$ every 3 years. If you made a $\$ 2000$ investment, how much money would you have after 45 years?
Future Amount $=[?](1+[])$
Future Amount $=\mathrm{I}(1+r)^{\mathrm{t}}$

Answer

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Answer

$\boxed{After 45 years, the investment would be worth approximately $64,060.18}$

Steps

Step 1 ：Calculate the number of time periods (3-year intervals) in 45 years: $\frac{45}{3} = 15$ time periods

Step 2 ：Use the compound interest formula: Future Amount = Initial Investment * $(1 + Interest Rate)^{Time Periods}$

Step 3 ：Plug in the values: Future Amount = $2000 * (1 + 0.26)^{15}$

Step 4 ：Calculate the future amount: Future Amount = $2000 * (1.26)^{15}$ = 64060.182624413

Step 5 ：$\boxed{After 45 years, the investment would be worth approximately $64,060.18}$