(a) state whether the problem relates to an ordinary annuity or an annuity due and then (b) solve the problem.

Jake Werkheiser decides to invest $\$ 2000$ in an IRA at the end of each year for the next $10$ years. If he makes these investments and if the certificates pay $12 \%$ compounded annually, how much will he have at the end of the $10$ years?

If Ben invests 4000 dollars at 4 percent interest per year, how much additional money must he invest at $5 \frac{1}{2} \%$ annual interest to ensure that the interest he receives each year is $4 \frac{1}{2} \%$ of the total amount invested?.

Sally invests some money at 6%/a compounded annually. After 5 years, she takes the principal and interest and reinvests it all at 7.2%/a compounded quarterly for 6 more years. At the end of this time, her investment is worth $14 784.56. How much did Sally originally invest?

Explain how you made your decision for this exercise.

Conjecture whether the equation $\tan x+\tan (2 x)+\tan (\pi-3 x)=$ $\tan x \cdot \tan (2 x) \cdot \tan (\pi-3 x)$ is an identity.

If you invest $P$ dollars in a bank account at an annual interest rate of $r \%$, then after $t$ years you will have $B$ dollars, where

$$B=P\left(1+\frac{r}{100}\right)^t .$$

$\bull$ Determine $d B / d t$, assuming $P$ and $r$ are constant. In terms of money, what does $d B / d t$ represent?

Given sentence below refers to a numbered sentence in the passage. Write the letter of the choice that gives the sentence a meaning that is closest to the original sentence.

There was no need for a(n).......... of citizens to vote on the decision.

a. accusation

b. minimum number

c. ballot

d. harmful event

Solve each problem that has a solution. If a problem has no solution, explain why. Isabel invested $8000, part in an account paying 6% interest and part in bonds paying 8%. If she had reversed the amounts invested, she would have received$100 less. How much did she invest in each?

If you invest P dollars in a bank account at an annual interest rate of r%, then after t years you will have B dollars, where $B=P\left(1+\frac{r}{100}\right)^{t}$. Find dB/dt, assuming P and r are constant. In terms of money, what does dB/dt represent?

(a) state whether the problem relates to an ordinary annuity or an annuity due and then (b) solve the problem.

Sofia can deposit $\$ 350$ at the beginning of each month into an account that earns $4.2 \%$ compounded monthly. How long before the account contains $\$ 17,000$?

Luc invests $\$ 7000$ in two bank accounts. One earns $1.5 \%$ simple interest per year, and the other earns $2.5 \%$ simple interest per year. After one year the total interest earned on these investments is $\$ 120.25$. How much money did he invest in each account ?

A man with $\$ 20,000$ to invest decides to diversify his investments by placing $\$ 10,000$ in an account that earns $7.2 \%$ compounded continuously and $\$ 10,000$ in an account that earns $8.4 \%$ compounded annually. Use graphical approximation methods to determine how long it will take for his total investment in the two accounts to grow to $\$ 35,000$.

Alex expects to graduate in 3.5 years and hopes to buy a new car then. He will need a 20% down payment, which amounts to $3600 for the car he wants. How much should he save now to have$3600 when he graduates if he can invest it at 6% compounded monthly?

On the line before each of the following sentences, write the correct form of the underlined pronoun if it is incorrect. If the underlined pronoun is already correct, write $C$
Please notify Paula or $\text{\underline{he}}$ about your decision.

If you invest $P$ dollars in a bank account at an annual interest rate of $r \%$, then after $t$ years you will have $B$ dollars, where

$$B=P\left(1+\frac{r}{100}\right)^t .$$

$\bull$ Determine $d B / d r$, assuming $P$ and $t$ are constant. In terms of money, what does $d B / d r$ represent?