The formula for calculating the future value of an interest earning account is

,

where

= future value,

= present value,

= annual interest rate,

= number of times the interest is compounded per year, and

= the number of years that have passed.

The problem asks for the amount of money in the account after 5 years, with 10% interested compounded four times per year (quarterly).

Plug in the given quantities and simplify:

The formula for finding the future value of an investment is

,

where

= future value,

= present value,

= interest rate, and

= number of times interest is compounded.

Plug in the given numbers and solve for the present value:

Initial amount = 5000

The account earns 4% compounded yearly ===> Each $1.00 will grow into $1.04.

Growth rate = 1.04

Jamie will withdraw the money after 5 years. Since the interest is compounded yearly, the number of periods is equal to the number of years the money will be in the account.

number of periods = 5

From the above information, we can calculate the amount accumulated (or final amount) after 5 years using the following formula:

final amount = initial amount * (growth rate)^{number of periods}

The formula for computing interest is:

Beginning Amount x ((1 + rate)^number of years) = Ending Amount After number of years

Make sure to convert the rate from percent to number: 3% = 0.03

So the answer is 

Using the equation for continuous compound interest and the given information, we get 

   is the compound interest formula where

P = Initial deposit = 5000

r = Interest rate = 0.12

n = Number of times interest is compounded per year = 1

t = Number of years that have passed = 5

Round to the nearest cent or hundredth is .

To determine Julio's account balance, we must use the interest formula given below:

where P is his principal (initial) investment, r is the interest rate (as a decimal), n is the number of times the interest is compounded, and t is the amount of time elapsed.

Plugging in all of our given information into the above formula - knowing that quarterly means four times a year - we get

To find the balance, B, of a continuously compounded interest account after a certain amount of time, we must use the following formula:

, where P is the initial investment, r is the interest rate (as a decimal), and t is the amount of time being considered.

Plugging in all of the given information, we get

which rounded becomes $2102.54

The formula to find the balance, B, of a continuously compounded interest account with interest rate, r, after a certain time, t, is given by

To solve this problem, we need to know only the initial investment (P), our final balance (three times P) and the interest rate (expressed as a decimal), 0.019.

Plugging in our known information into the formula for continuously compounded interest, we get

We now solve for t:

Exponentiating both sides allows us to get rid of the exponential:

To determine the amount of time needed to double the initial investment - P - into a compound interest account, we simply plug in our given information into the formula:

where B is the balance, P is the initial investment, r is the interest rate (as a decimal), n is the number of times the interest is compounded, and t is the time elapsed.

Now, because we are doubling P, our balance B becomes two times P:

Now, we can solve for P:

To bring the time variable down from being an exponent, we take the logarithm of both sides (common or natural):