Question 874076
A = P * (1 + (r/n))^(n*t)


replace what you know in the formula and solve for what you don't know.


what you know:


r = 6% divided by 100% = .06 because r is always the decimal equivalent of the % which is always the percent divided by 100%.



n = 4 because there are 4 compounding periods per year (quarterly compounding).


r/n = .06 / 4 = .015


P = $500.


the formula is, once again:


A = P * (1+(r/n)^(n*t


you are given that A is going to be a quadruple of P which means that A will be equal to 4 * $500, so A is equal to $2000.


to summarize what you know:


n = 4
r = .06
r/n = .015
P = $500
A = $2000
t = unknown since that what you need to solve for.


your formula of:


A = P * (1 + (r/n))^(n*t) becomes:


$2000 = $500 * (1 + .015)^4t which becomes:


$2000 = $500 * (1.015)^4t


divide both sides of this formula by $500 to get:


$2000 / $500 = (1.015)^4t


simplify to get:


4 = (1.015)^4t


since the unknown is in the exponent, this calls for using logarithms to solve for it.


take the log of both sides of this equation to get:


log(4) = log((1.015)^4t)


use law of logarithms formula number 1 (shown below the final answer) to convert this equation to:


log(4) = 4t * log(1.015)


divide both sides of this formula by log(1.015) to get:


log(4) / log(1.015) = 4t


use your calculator to solve for 4t to get:


4t = 93.11105126


divide both sides of this equation by 4 to get:


t = 23.27776282


that's your final answer.


logarithm law number 1 is equal to:


log(x^a) = a * log(x)


in your problem, a was equal to 4t and x was equal to 1.015.


that's how you got log(1.015^4t) = 4t*log(1.015)


to confirm your answer is correct, substitute for t in the original equation to see if that equation becomes true.


the original equation is:


$2000 = $500 * (1.015)^4t


replace t with 23.27776282 to get:


$2000 = $500 * (1.015)^(4 * 23.27776282)


simplify the right side of this equation to get:


$2000 = $2000.


This confirms the solution is good.


the solution is:


t = 23.27776282 which you can round off to 23.28 years depending on how accurate you need the solution to be.