Nathaniel invested $2,900 in an account paying an interest rate of 5.4% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 11 years?
The answer is A≈5252.53
2900e^(0.054*11)
To solve this problem, we can use the formula for compound interest when the interest is compounded continuously:
A = P * e^(rt)
Where:
A is the final amount of money in the account
P is the initial principal (or amount invested)
e is the mathematical constant approximately equal to 2.71828
r is the interest rate (in decimal form)
t is the time period (in years)
Now let's plug in the values for the given problem:
P = $2,900
r = 5.4% = 0.054 (interest rate expressed as a decimal)
t = 11 years
A = $2,900 * e^(0.054 * 11)
To the nearest cent, we can use a calculator or an online tool to calculate the value of "e^(0.054 * 11)" and then multiply it by $2,900 to find the final amount A.
After performing the calculations, the amount of money in the account after 11 years would be approximately $5,269.98.