An investment is advertised as returning 4.5% every 6 months (semiannually), compounded semiannually. If $30,000 is invested, the growth can be modeled by the equation A(t) = 30,000(1.045)2t. What is the equivalent annual growth rate for this investment (rounded to the nearest tenth of a percent) and what is it worth (rounded to the nearest thousand dollar) after 30 years?

Hint: Find the value of 1.0452 on your calculator.

Question

An investment is advertised as returning 4.5% every 6 months (semiannually), compounded semiannually. If $30,000 is invested, the growth can be modeled by the equation A(t) = 30,000(1.045)2t. What is the equivalent annual growth rate for this investment (rounded to the nearest tenth of a percent) and what is it worth (rounded to the nearest thousand dollar) after 30 years?

Hint: Find the value of 1.0452 on your calculator.

mathmale · Answer

It's really important that you learn to express exponentiation properly.  Your 
A(t) = 30,000(1.045)2t seems to imply multiplication all the way through, which is not correct.

Please use Equation Editor or the Draw utility, or the ' ^ ' symbol, to express exponentiation.

$$Right:  A(t) = 30,000(1.045)^{2t}$$

Wrong:  A(t) = 30,000(1.045)2t

mathmale · Answer

If you wish to take the hint given you, evaluate (1.045)^2 on your calculator.

Type in 1.045.  Then press the calculator key that looks like   ^    .

Your answer?

anonymous · Answer

Hi there, yes I see what you mean

anonymous · Answer

i have to show the exponents correctly, thank you for the tip!