Suppose you invest $700 at an annual interest rate of 7.6% compounded continuously. How much will you have in the account after 1.5 years?
The formula is:
P(1+r)^n
Where p is the principal amount (or amount you start with)
r is the rate (.076)
and n is the frequency in years
To calculate the amount you will have in the account after 1.5 years with continuous compounding, you can use the formula:
A = P * e^(rt)
Where:
A = the final amount in the account
P = the initial principal (investment)
e = the mathematical constant approximately equal to 2.71828
r = the annual interest rate (expressed as a decimal)
t = the time period in years
In this case, your initial principal (investment) is $700, the annual interest rate is 7.6% (or 0.076 as a decimal), and the time period is 1.5 years.
Plugging these values into the formula:
A = 700 * e^(0.076 * 1.5)
To calculate this using a calculator, follow these steps:
1. Enter 0.076 * 1.5.
2. Press the exponent button (^) or key.
3. Enter the value of e (approximately 2.71828).
4. Press the equals (=) button.
The calculator will give you the result of e^(0.076 * 1.5).
Now, multiply this result by 700:
A ≈ 700 * e^(0.076 * 1.5) ≈ $770.99
Therefore, you will have approximately $770.99 in the account after 1.5 years with continuous compounding.