How long does it take for an investment to double its value if the interest is 7.25% compounded continuously?

9.9 years

Step-by-step explanation:

We have an interest of 7.25%, compounded continuously, we can write this as:

P = A*e^(r*n)

where:

P is the total balance after n years.

A is the initial investment.

r is the ratio of increase, in the case of a continuous compound, this will be:

r = Ln(1 + 7.25%/100%) = Ln(1 + 0.0725) = 0.070

n is the time in years.

Then we want to have our initial investement doubled, this means:

P = 2*A

let's find n for this situation:

P = 2*A = A*e^(0.070*n)

     2 = e^(0.070*n)

Now we can apply the Ln() to both sides, remember that:

Ln(e^x) = x

Then:

 2 = e^(0.070*n)

Ln(2) = Ln(e^(0.070*n)) = 0.070*n

Ln(2)/0.070 = 9.9

So we need 9.9 years to double the initial investment.

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98

where did you get them? if you picked from the grass, is is probably poisonous.

step-by-step explanation: