# An investment program was set up using an annuity due with payments of $1,200 at the beginning of each quarter. Consider payments for 5 years are made into an account expected to pay 8% compounded quarterly. What is the amount of annuity? # An investment program was set up using an annuity due with payments of$1,200 at the beginning of each quarter. Consider payments for 5 years are made into an account expected to pay 8% compounded quarterly. What is the amount of annuity?

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An investment program was set up using an annuity due with payments of $1,200 at the beginning of each quarter. Consider payments for 5 years are made into an account expected to pay 8% compounded quarterly. What is the amount of annuity? ## Answers (1) 2021-03-10 Use the formula: $$\displaystyle{A}={C}\frac{{{\left({1}+{i}\right)}^{{n}}-{1}}}{{i}}$$ Substitute from the given $$\displaystyle{A}=\{1200}\frac{{{\left({1}+{0.08}\right)}^{{20}}-{1}}}{{0.08}}$$ =$54,914.35

### Relevant Questions

How long does it take for an investment to double in value if it is invested at $$14\%$$ compounded quarterly and compounded continuously?
a) At $$14\%$$ compounded quarterly, the investment doubles in how many years?
b) At $$14\%$$ compounded continuously, the investment doubles in how many years?
The dominant form of drag experienced by vehicles (bikes, cars,planes, etc.) at operating speeds is called form drag. Itincreases quadratically with velocity (essentially because theamount of air you run into increase with v and so does the amount of force you must exert on each small volume of air). Thus
$$\displaystyle{F}_{{{d}{r}{u}{g}}}={C}_{{d}}{A}{v}^{{2}}$$
where A is the cross-sectional area of the vehicle and $$\displaystyle{C}_{{d}}$$ is called the coefficient of drag.
Part A:
Consider a vehicle moving with constant velocity $$\displaystyle\vec{{{v}}}$$. Find the power dissipated by form drag.
Express your answer in terms of $$\displaystyle{C}_{{d}},{A},$$ and speed v.
Part B:
A certain car has an engine that provides a maximum power $$\displaystyle{P}_{{0}}$$. Suppose that the maximum speed of thee car, $$\displaystyle{v}_{{0}}$$, is limited by a drag force proportional to the square of the speed (as in the previous part). The car engine is now modified, so that the new power $$\displaystyle{P}_{{1}}$$ is 10 percent greater than the original power ($$\displaystyle{P}_{{1}}={110}\%{P}_{{0}}$$).
Assume the following:
The top speed is limited by air drag.
The magnitude of the force of air drag at these speeds is proportional to the square of the speed.
By what percentage, $$\displaystyle{\frac{{{v}_{{1}}-{v}_{{0}}}}{{{v}_{{0}}}}}$$, is the top speed of the car increased?
Express the percent increase in top speed numerically to two significant figures.
What are the future value and the interest earned if $$3000$$ is invested for 6 years at $$8\%$$ compounded quarterly?
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b) How much total interest would Bethany pay at $$5%$$ interest compounded continuously?
c) Which option results in less total interest?
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a) What is the radius of an equipotential surface having apotential of 30 V?
b) Are surfaces whose potentials differ by a constant amount (1.0V,say) evenly spaced?
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