Suppose you invest $5000 at an annual rate of 4% compounded continuously how much will be in the account after 5 years?
5000*e^(5*.04) = $6107
$6083.26
To calculate the amount in the account after 5 years, we can use the continuous compound interest formula:
A = P * e^(rt)
Where:
A is the final amount in the account
P is the principal amount (initial investment)
r is the annual interest rate (as a decimal)
t is the time in years
e is the base of the natural logarithm (approximately 2.71828)
Given:
P = $5000
r = 4% = 0.04 (since it is a decimal)
t = 5 years
Let's plug these values into the formula and calculate:
A = 5000 * e^(0.04 * 5)
First, we'll calculate the exponential part:
e^(0.04 * 5) ≈ 1.2214
Now, we'll multiply the exponential part with the principal amount:
A ≈ 5000 * 1.2214
A ≈ 6107
Therefore, the amount in the account after 5 years will be approximately $6107.
To find the amount in the account after 5 years with continuous compounding, we can use the formula:
A = P * e^(rt)
Where:
A = the amount in the account after time t
P = the initial principal (initial investment)
e = the mathematical constant approximately equal to 2.71828
r = the annual interest rate (as a decimal)
t = the time period (in years)
In this case, the initial principal (P) is $5000, the annual interest rate (r) is 4% (or 0.04 as a decimal), and the time period (t) is 5 years.
Plugging in the values, we have:
A = 5000 * e^(0.04*5)
Now we can calculate the amount in the account after 5 years.