The Compound Interest Question

THE QUESTION Prudence had $750 she invested in the bank. The teller said that the money she invested earned interest at the rate of 9%, compounded continuously. How long will it take for the investment to triple? Quadruple?

Prudence had $750 she invested in the bank. The teller said that the money she invested earned interest at the rate of 9%, compounded continuously. How long will it take for the investment to triple? Quadruple?

.:. WHAT WE KNOW .:. GENERAL COMPOUND [CONTINUOUS] INTEREST FORMULA: A = Pe rt , where A = total amount, P = principal amount, e = constant, r = rate of interest and t = period of time to get amount. P = $750 r = 9% = 0.09 tripled amount = ($750)(3) = $2250 quadrupled amount = ($750)(4) = $3000

GENERAL COMPOUND [CONTINUOUS] INTEREST FORMULA: A = Pe rt , where A = total amount, P = principal amount, e = constant, r = rate of interest and t = period of time to get amount.

P = $750

r = 9% = 0.09

tripled amount = ($750)(3) = $2250

quadrupled amount = ($750)(4) = $3000

THE SOLUTION

STEPS PROCESS The first thing the question asked for was the amount of time to triple the initial investment. This means the total amount will equal three times the initial amount, which is $2250. Plug the given information into the formula and it is found that the only variable missing is the time. In order to find the time, the value must be isolated. This is done by dividing out the initial amount and finding the ln of both sides to remove e. Once e is removed, multiply the reciprocal of r to both sides, allowing t to remain.

STEPS

PROCESS

The first thing the question asked for was the amount of time to triple the initial investment. This means the total amount will equal three times the initial amount, which is $2250.

Plug the given information into the formula and it is found that the only variable missing is the time.

In order to find the time, the value must be isolated. This is done by dividing out the initial amount and finding the ln of both sides to remove e. Once e is removed, multiply the reciprocal of r to both sides, allowing t to remain.

STEPS PROCESS The second part of the question asked for the amount of time to quadruple the initial investment. This means the total amount will equal 4x the initial amount, which is $3000. Plug the given information into the formula. In order to find the time, the value must be isolated. This is done by dividing out the initial amount and finding the ln of both sides to remove e. Once e is removed, multiply the reciprocal of r to both sides, allowing t to remain.

STEPS

PROCESS

The second part of the question asked for the amount of time to quadruple the initial investment. This means the total amount will equal 4x the initial amount, which is $3000.

Plug the given information into the formula.

In order to find the time, the value must be isolated. This is done by dividing out the initial amount and finding the ln of both sides to remove e. Once e is removed, multiply the reciprocal of r to both sides, allowing t to remain.

Dear Prudence… We learned a lot about her today…and our responsibility as friends is to take care of her… My Garden Flowers by flickr user chalkie_colour_cir cles'

We learned a lot about her today…and our responsibility as friends is to take care of her…