(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?

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

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

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?

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

(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) 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?

A recent college graduate buys a new car by borrowing $\$ 18,000$ at $8.4 \%$ compounded monthly for $5$ years. She decides to pay $\$ 384$ instead of the monthly payment required by the loan.

(a) What is the monthly payment required by the loan, and how much extra did she pay per month?

(b) How many $\$ 384$ payments will she make to pay off the loan?

( c ) How much will she save by paying $\$ 384$ per month rather than the required payment?

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 $R: \quad 80,000=R\left[\frac{(1+0.04)^{30}-1}{0.04}\right]$

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?

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

The loudness $L(x),$ measured in decibels (dB), of a sound of intensity x, measured in watts per square meter, is defined as $L(x)=10 \log \frac{x}{I_{0}},$ where $I_{0}=10^{-12}$ watt per square meter is the least intense sound that a human ear can detect. Determine the loudness, in decibels, of each of the following sounds. Normal conversation: intensity of $x=10^{-7}$ watt per square meter.