Lauren plans to deposit $5000 into a bank account at the beginning of next month and $175/month into the same account at the end of that month and at the end of each subsequent month for the next 3 years. If her bank pays interest at a rate of 3%/year compounded monthly, how much will Lauren have in her account at the end of 3 years

$12,053.86

Explanation:

The easiest way to calculate this is using an excel spreadsheet and the future value function. Using the FV function =FV(rate,nper,pmt)

This function will give us the future value of the annuity =FV(0.25%,36,175) = $6,583.60

Now we must add the future value of the original $5,000:

future value = $5,000 x (1 + 0.0025)³⁶ = $5,470.26

total future value = $6,583.60 + $5,470.26 = $12,053.86

if you do not want to use an excel spreadsheet, you can use the following formula:

F = P x ([1 + r]ⁿ - 1 )/r

F = 175 x [(1 + 0.0025)³⁶ - 1] / 0.0025 = $6,583.60

the answer will be the same

sound is invisible, but sometimes we can feel it. when a kettle-drum is thumped with a stick that time the tight drum skin moving up and down very quickly for some time and then it pumped sound waves into the air. loudspeakers also work in a similar manner.

components of a speaker:

electromagnet

in order to translate an electrical signal into an audible sound, an electromagnet is used in looudspeakers

  suspension

suspension is used to   center the voice coil in the gap of the magnet and it exerts a restoring force to keep it there. suspension is used to limits the maximum mechanical excursion of the diaphragm and voice coil.

voice coil

voice coil is a coil of wire which is attached to the apex of a loudspeaker cone. it provides the motive force to the cone by the reaction of a magnetic field to the current passing through it.

cone

in a   loudspeaker, a   thin, semi-rigid membrane attached to the voice coil, which moves in a magnetic gap due to which it vibrates   and produced sound. it is known as diaphragm and it can also be called a cone, though not all speaker diaphragms are cone-shaped.

surround

surround is also known as front suspension. surround is used to join the cone to the chassis. together with the suspension it controls the cone excursion, and it is also used to   determine how energy which is   travelling through the cone is absorbed, and how the speaker limits when it reaches the ends of its travel.

dustcap

dustcap is used to protect the voice coil from dust and dirt. it is a part of the cone.

how speaker work

the outer part of the cone is fastened to the outer part of the loudspeaker's circular metal rim. the inner part is fixed to   voice coil that sits just in front of a permanent magnet . when loudspeaker is hooked up to a stereo, electrical signals feed through the speaker cables into the coil. it will convert the coil into an electromagnet magnet . when electricity flows back and forth in the cables, the electromagnet either repels or attract the permanent magnet. this moves the coil back and forth, and it pull and push the loudspeaker cone. like a drum skin vibrating back and forth, the moving cone pumps sounds out into the air.in this way loudspeakers works.