Find the present value of an annuity due that pays $\$ 25,000$ every $6$ months for the next $2 \frac{1}{2}$ years if money is worth $6.2 \%$ compounded semiannually.

Future value What is the future value if $\$ 1000$ is invested for $6$ years at $8 \%$ compounded continuously?

Determine the requested value (to the nearest dollar), and tell what each of the other values represents. Determine $A_n: A_n=2550\left[\frac{1-(1+0.01)^{-120}}{0.01}\right]$

A universal set U consists of 12 elements. If sets A, B, and Care proper subsets of U and n(U)=12, n(AnB)=n(AnC)=n(BnC)=6, n(AnBnC)=4, and n(AUBUC)=10, determine (a) n(AUB), (b) n(A'UC), (c) n(AnB)'

Determine the requested value (to the nearest dollar), and tell what each of the other values represents. Determine $S: \quad S=1000\left[\frac{(1+0.03)^{25}-1}{0.03}\right]$

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 woman buys an apartment house for $\$ 1,250,000$ by making a down payment of $\$ 250,000$ and amortizing the rest of the purchase price with monthly payments over the next $10$ years. The interest rate on the debt is $7.2 \%$ compounded monthly.

Use the approach in Gauss's Problem to find the following sums of arithmetic sequences (do not use formulas): a. 1+2+3+4+...+49 b. 1+3+5+7+...+2009 c. 6+12+18+...+600 d. 1000+995+990+...+5

Use the approach in Gauss's Problem to find the following sums of arithmetic sequences: a. 1+2+3+4+...+998 b. 1+3+5+7+...+ 101 c. 4+9+14+19 +... +494 d. 881+872+863+854+..+8

a. The sum of the sequence is $\square$.

What are the dimensions of the rectangular box, open at the top, that has maximum volume when the surface area is 48?

A rectangular box with a square base and no top is to be made of a total of 120 cm sq. of cardboard.

a. Find the dimensions of the box of maximum volume.

b. Make a conjecture about the depth of the maximum-volume box in relation to the base length if the box has a fixed surface area.

(a) How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once? (b) How many of these are odd numbers? (c) How many are greater than 330?

Figure shows P(t), the percentage of inventory of an item that has sold by time t, where t is in days and day 1 is January 1. (a) When did the first item sell? The last item? (b) On May 1 (day 121), what percentage of the inventory had been sold? (c) Approximately what percentage of the inventory sold during May and June (days 121-181)? (d) What percentage of the inventory remained after half of the year had passed (at day 181)? (e) Estimate when items went on sale and sold quickly.

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.

Sean Lee purchases $\$ 20,000$ worth of supplies for his restaurant by making a $\$ 3000$ down payment and amortizing the remaining cost with quarterly payments over the next $5$ years. The interest rate on the debt is $16 \%$ compounded quarterly.

Use five steps of Euler's method to determine an approximate solution for the differential equation $d y / d x=y-x$ with initial condition $y(0)=10$, using step size $\Delta x=0.2$. What is the estimated value of $y$ at $x=1?$