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

A $\$ 2.4$ million state lottery pays $\$ 10,000$ at the beginning of each month for $20$ years. How much money must the state actually have on hand to set up the payments for this prize if money is worth $6.3 \%$ compounded monthly?

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 $\$ 60,000$ ?

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

Recent sales of some real estate and record profits make it possible for a manufacturer to set aside $\$ 800,000$ in a fund to be used for modernization and remodeling. How much can be withdrawn from this fund at the beginning of each half-year for the next $3$ years if the fund earns $7.7 \%$ compounded semiannually?

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

(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 $\$ 50,000$ ?

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?

For life insurance policies, some of the premium pays for the cost of the insurance and the remainder goes toward the cash value of the policy and earns interest like a savings account. Suppose that on the cash value of their policies, one insurance company pays $4.8 \%$ compounded monthly and another pays $4.82 \%$ compounded semiannually. Which company offers a higher yield?

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

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 $P: 9600=P+P(0.05)(4)$

Construction fund A company wants to have $\$ 250,000$ available in $4 \frac{1}{2}$ years for new construction. How much must be deposited at the beginning of each quarter to reach this goal if the investment earns $10.2 \%$ compounded quarterly?

(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 $P: \quad 25,000=P(1+0.03)^{48}$