(a) The purchase of Alaska cost the United States $\$ 7$ million in $1869$. If this money had been placed in a savings account paying $6 \%$ compounded annually, how much money would have been available from this investment in $2015$?

(b) If the $7 million earned 7% compounded annually since$1869$, how much would have been available in$2015$?

( c ) Do you think either amount would have purchased Alaska in$2015$? Explain in light of the value of Alaska's resources or perhaps the price per acre of land.

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

A sinking fund is established by a working couple so that they will have $\$ 60,000$ to pay for part of their daughter's education when she enters college. If they make deposits at the end of each $3$-month period for $10$ years and if interest is paid at $12 \%$ compounded quarterly, what size deposits must they make?

A 10-year Emmaco Corporate bond has a par value of $\$ 10,000$ with coupons at $7.8 \%$ paid semiannually.

(a) If this bond is bought to yield $10 \%$ compounded semiannually, find its price.

(b) Suppose that after this bond has been held for $2$ years, the desired yield is $8 \%$ compounded semiannually. Find the selling price.

Find the sum of the first $38$ terms of the arithmetic sequence with first term $2$ and $38$th term $113$.

(a) A $40$-year-old man has $\$ 432,860$ in an IRA account. He decides to make no additional contributions to the account but expects it to grow at $7.5 \%$ compounded annually. How much does he expect to have in the account when he retires at age $62$?

(b) How much more money would the man have if his investments earned $8.5 \%$ compounded annually?

A debt of $\$ 280,000$ is amortized with $40$ equal semiannual payments of $\$ 14,357.78$. If interest is $8.2 \%$ compounded semiannually, find the unpaid balance of the debt after $25$ payments have been made.

Find the $73$rd term of the arithmetic sequence with first term $20$ and $10$th term $47$.

A recent graduate's student loans total $\$ 18,000$. If these loans are at $4.2 \%$ compounded quarterly for $10$ years, what are the quarterly payments?

Find the $36$th term of the arithmetic sequence with third term $10$ and eighth term $25$.

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

A retiree inherits $\$ 93,000$ and invests it at $6.6 \%$ compounded monthly in an annuity that provides an amount at the end of each month for the next $12$ years. Find the monthly amount.

Determine the requested value and tell what the other numbers represent. Determine $P: 11,800=P+P(0.03)(6)$

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

A company establishes a sinking fund to discharge a debt of $\$ 750,000$ due in $8$ years by making equal semiannual deposits, the first due in $6$ months. If the investment pays $12 \%$ compounded semiannually, what is the size of the deposits?

The problem is complex financial problems that require several skills, perhaps some from previous sections.

During four years of college, Nolan MacGregor's student loans are $\$ 4000, \$ 3500, \$ 4400$, and $\$ 5000$ for freshman year through senior year, respectively. Each loan amount gathers interest of $1 \%$ compounded quarterly while Nolan is in school and $3 \%$ compounded quarterly during a $6$-month grace period after graduation.

(a) What is the loan balance after the grace period? Assume that the freshman year student loan costs Nolan $1 \%$ interest for $3 / 4$ year during the first year, then for $3$ full years until graduation. Make similar assumptions for the loans for the other years.

(b) After the grace period, the loan is amortized over the next $10$ years at $3 \%$ compounded quarterly. Find the quarterly payment.

( c ) If Nolan decides to pay an additional $\$ 90$ per payment, how many payments will amortize the debt? What amount should be added to the last payment to pay the loan in full?

(d) How much will Nolan save by paying the extra $\$ 90$ with each payment?

To help their son buy a car on his $16$th birthday, a boy's parents invest $\$ 7500$ on his 10th birthday. If the investment pays $9 \%$ compounded continuously, how much is available on his $16$th birthday?