A couple who borrow $\$ 90,000$ for $30$ years at $7.2 \%$ compounded monthly must make monthly payments of $\$ 610.91$.

(a) Find their unpaid balance after $1$ year.

(b) During that first year, how much interest do they pay?

A debt of $\$ 8000$ is to be amortized with $8$ equal semiannual payments of $\$ 1288.29$. If the interest rate is $12 \%$ compounded semiannually, find the unpaid balance immediately after the fifth payment.

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?

A homeowner planning a kitchen remodeling can afford a $\$ 600$ monthly payment. How much can the homeowner borrow for $5$ years at $6 \%$ compounded monthly and still stay within the budget?

Describe a debt to be amortized. In each problem, find: (a) the size of each payment,

(b) the total amount paid for each purchase,

( c ) the total interest paid over the life of the loan.

A man buys a house for $\$ 350,000$. He makes a $\$ 150,000$ down payment and amortizes the rest of the purchase price with semiannual payments over the next $10$ years. The interest rate on the debt is $12 \%$ compounded semiannually.

Amount of an Annuity For 8 years, Yvette deposits $100 at the end of each month into an annuity paying 6% annual interest compounded monthly.

Find the total amount Yvette deposits into the account over the 8 years.

The terms of a single parent's will indicate that a child will receive an ordinary annuity of $\$ 16,000$ per year from age $18$ to age $24$ (so that the child can attend college) and that the balance of the estate goes to a niece. If the parent dies on the child's $14$th birthday, how much money must be removed from the estate to purchase the annuity? (Assume an interest rate of $6 \%$ compounded annually.)

A couple purchasing a home budget $\$ 1800$ per month for their loan payment. If they have $\$ 20,000$ available for a down payment and are considering a $25$-year loan, how much can they spend on the home at each of the following rates?

(a) $6.9 \%$ compounded monthly

(b) $7.5 \%$ compounded monthly

Six-and-a-half years ago a small business borrowed $\$ 50,000$ for $10$ years at $9 \%$ compounded semiannually to update some equipment. Now the company would like to pay off this loan. Find the payoff amount just after the company makes the $14$th semiannual payment of $\$ 3843.81$.

Compute the simple interest for specified length of time and future value at the end of that time (in dollars). Round all answers to the nearest cent.

$3,000 is invested for 2 years at 7% per year.

Find the present value of the given investment. An investment earns 6% per year and is worth $30,000 after 20 months.

For equipment upgrades, a business borrowed $\$ 400,000$ at $8 \%$ compounded semiannually for $5$ years. What are the semiannual payments?

Compute the specified quantity. Round all answers to the nearest month, the nearest cent, or the nearest 0.001%, as appropriate. A $4,000 loan, taken now, with a simple interest rate of 8% per year, will require a total repayment of$4,640. When will the loan mature?

You take out an 8-month, $9,000 loan at 8% simple interest. How much would you owe at the end of the 8 months? (Round your answer to the nearest cent.)