Time to reach a goal If $\$ 1200$ is deposited at the end of each quarter in an account that earns $7.2 \%$ compounded quarterly, how long will it be until the account is worth $\$ 60,000$ ?

Annuity Find the future value of an annuity due of $\$ 800$ paid at the beginning of every $6$-month period for $10$ years, if it earns interest at $12 \%$ compounded semiannually.

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

A couple has determined that they need $\$ 1.5$ million to establish an annuity when they retire in $25$ years. How much money should they deposit at the end of each month in an investment plan that pays $10 \%$ compounded monthly, so that they will have the $\$ 1.5 \mathrm{mil}$ lion in $25$ years?

A debt of $\$ 8000$ is to be amortized with $8$ equal semiannual payments. If the interest rate is $12 \%$ compounded semiannually, what is the size of each payment?

Determine the requested value (to the nearest dollar), and tell what each of the other values represents. Determine $R: 135,000=R\left[\frac{1-(1+0.005)^{-360}}{0.005}\right]$

Write the first four terms and the 10 th term of the sequence whose $n$th term is

$$a_n=\frac{n-4}{n(n+2)}$$

Find the $80$th term of the arithmetic sequence with first term $-2$ and common difference $3$.

Determine the requested value and tell what the other numbers represent. Determine $P: 9600=P+P(0.05)(4)$

Write the first five terms of the sequence whose $n$th term is $a_n=(-1)^n /\left(n^2\right)$.

To buy a municipal bond that matures to $\$ 10,000$ in $9$ months, you must pay $\$ 9510$. What simple interest rate is earned?

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

As a result of a court settlement, an accident victim is awarded $\$1.2$ million. The attorney takes one-third of this amount, another third is used for immediate expenses, and the remaining third is used to set up an annuity. What amount will this annuity pay at the beginning of each quarter for the next 5 years if the annuity earns $7.6 \%$ compounded quarterly?

Determine the requested value and identify each of the other values as the periodic rate, the number of periods, the principal, or the future value. Determine $P: \quad 25,000=P(1+0.03)^{48}$

Determine the requested value (to the nearest dollar), and tell what each of the other values represents. Determine $R: \quad 80,000=R\left[\frac{(1+0.04)^{30}-1}{0.04}\right]$

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

If $\$ 2000$ is deposited at the end of each quarter into an account that earns $6 \%$ compounded quarterly, how long until the account reaches $\$ 50,000$ ?