4.1 Exponential functions  (Page 11/16)

After a certain number of years, the value of an investment account is represented by the equation $10,250{\left(1+\frac{0.04}{12}\right)}^{120}.$ What is the value of the account?

What was the initial deposit made to the account in the previous exercise?

How many years had the account from the previous exercise been accumulating interest?

An account is opened with an initial deposit of $6,500 and earns $3.6\%$ interest compounded semi-annually. What will the account be worth in $20$ years?

How much more would the account in the previous exercise have been worth if the interest were compounding weekly?

Solve the compound interest formula for the principal, $P$ .

Use the formula found in the previous exercise to calculate the initial deposit of an account that is worth $\$14,472.74$ after earning $5.5\%$ interest compounded monthly for $5$ years. (Round to the nearest dollar.)

How much more would the account in the previous two exercises be worth if it were earning interest for $5$ more years?

Use properties of rational exponents to solve the compound interest formula for the interest rate, $r.$

Use the formula found in the previous exercise to calculate the interest rate for an account that was compounded semi-annually, had an initial deposit of $9,000 and was worth $13,373.53 after 10 years.

Use the formula found in the previous exercise to calculate the interest rate for an account that was compounded monthly, had an initial deposit of $5,500, and was worth $38,455 after 30 years.

$y=3742{\left(e\right)}^{0.75t}$

$y=150{\left(e\right)}^{\frac{3.25}{t}}$

$y=2.25{\left(e\right)}^{-2t}$

Suppose an investment account is opened with an initial deposit of $\$12,000$ earning $7.2\%$ interest compounded continuously. How much will the account be worth after $30$ years?

How much less would the account from Exercise 42 be worth after $30$ years if it were compounded monthly instead?

$f(x)=2{\left(5\right)}^x,$ for $f\left(-3\right)$

$f(x)=-4^{2x+3},$ for $f\left(-1\right)$

$f(x)=e^x,$ for $f\left(3\right)$

$f(x)=-2e^{x-1},$ for $f\left(-1\right)$

$f(x)=2.7{\left(4\right)}^{-x+1}+1.5,$ for $f\left(-2\right)$

$f(x)=1.2e^{2x}-0.3,$ for $f\left(3\right)$

$f(x)=-\frac{3}{2}{\left(3\right)}^{-x}+\frac{3}{2},$ for $f\left(2\right)$

$(0,3)$ and $(3,375)$

$(3,222.62)$ and $(10,77.456)$

$(20,29.495)$ and $(150,730.89)$

$(5,2.909)$ and $(13,0.005)$

$(\mathrm{11,310.035})$ and $(\mathrm{25,356.3652})$

The annual percentage yield (APY) of an investment account is a representation of the actual interest rate earned on a compounding account. It is based on a compounding period of one year. Show that the APY of an account that compounds monthly can be found with the formula $\text{APY}={\left(1+\frac{r}{12}\right)}^{12}-1.$