This exercise concerns a single investment of $10,000. Find the continuous interest rate per year, yielding a future value of$20,000 in the given time period. 60 years

Assume you make the following investments:

a. You invest $8,000 for five years at 14% interest. b. In a different account earning 14% interest, you invest$1,750 at the end of each year for five years.

Requirement

1. Rather than comparing the payout options at their present values (as done in the chapter), compare the payout options at their future value, 10 years from now. a. Using an 8% interest rate, what is the future value of each payout option? b. Rank your preference among payout options. c. Does computing the future value rather than the present value of the options change your preference between payout options? Explain your reasoning.

A block of wood floats on water. A layer of oil is then poured on top of the water to a depth that more than covers the block. Is the volume of wood submerged in the water greater than, less than, or the same as before the oil was added?

Consider heat loss through the two walls of a house on a winter night. The walls are identical, except that one of them has a tightly fit glass window. Through which wall will the house lose more heat? Explain.

Calculate the maximum value that could be obtained for the magnifying power of a simple magnifier, using Equation 32-20. Hint: Think about the smallest focal length lens that could be made from glass and still be used as a magnifier.

Indicate whether the statement is true or false:Assuming continuous growth rate of $3\%$, the future value five years from now of a $1000 payment today is$1000e^{0.15}$.

This exercise concerns a single investment of $10,000. Find the continuous interest rate per year, yielding a future value of$20,000 in the given time period. 20 years

Find the future value (to the nearest dollar) of the inflation-adjusted retirement account with $2\%$ annual inflation rate, $\$1000$ initial deposit, $6\%$ annual rate of return in $20$ years. Deposits are made at the end of each year.

A magnifying glass produces an angular magnification of $4.5$ when used by a young person with a near point of 18 $\mathrm{cm}$. Compute the maximum angular magnification obtained by an older person with a near point of $45 \mathrm{~cm}$ .

The present value of a perpetuity is equal to the payment on the annuity, PMT, divided by the interest rate, I:PV=PMT/I. What is the future value of a perpetuity of PMT dollars per year?

Suppose reflected white light is used to observe a thin transparent coating on glass as the coating material is gradually deposited by evaporation in a vacuum. Describe color changes that might occur during the process of building up the thickness of the coating.

A glass plate is sprayed with uniform opaque particles. When a distant point source of light is observed looking through the plate, a diffuse halo is seen whose angular width is about $2^{\circ}$. Estimate the size of the particles.

Cadmium ion in solution is analyzed by being precipitated as the sulfide, a yellow compound used as a pigment in everything from artists' oil paints to glass and rubber. Calculate the molar solubility of cadmium sulfide at $25^{\circ} \mathrm{C}$.

Annuity Find the future value of an annuity due of $\$ 800$ paid at the beginning of every $6$-month period for $10$ years, if it earns interest at $12 \%$ compounded semiannually.