Samuel invested $28,000 in an account paying an interest rate of 5% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 5 years?
Question
Samuel invested $28,000 in an account paying an interest rate of 5% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 5 years?
Solution
To solve this problem, we can use the formula for continuous compound interest, which is A = P * e^(rt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- t is the time the money is invested for, in years.
Given in the problem:
- P = $28,000
- r = 5% = 0.05 (in decimal form)
- t = 5 years
Substitute these values into the formula:
A = 28000 * e^(0.05*5)
Now, calculate the value:
A = 28000 * e^(0.25)
A = 28000 * 1.2840254167
A = $35952.71
So, to the nearest dollar, there would be $35,953 in the account after 5 years.
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