Question

Find a formula for value of V, an investment ($), initially worth $16000 that grows 12% every 7 years

Answer 1

The amount an investment of 16000 grows over 7 years is 16000*0.12 (i.e., 12% of 16000). So, the total amount after 7 years is 16000 + 16000*0.12, which is the same as writing 16000*1.12. Now, continue the same argument: the amount we now have 16000*1.12 grows after another 7 years to (16000*1.12)*1.12. Third 7-year period, again, (16000*1.12*1.12*)*1.12, and so on. As you can already see the number of periods shows up as the number of factors 1.12 multiplied here. A shorthand for writing that is to use the exponent, like this $16000\cdot 1.12^3$.

Generalizing to n 7-year periods yields a formula:

$V = 16000\cdot 1.12^n$