If the bank had been paying interest at the rate of 8% compounded continuously and he has $14,000 on deposit today, what was his initial deposit? (Round your answer to the nearest cent.)

Question

Diego deposited a certain sum of money in a bank 4 years ago.

Answer 1

Hi, Zen! I would solve this question as follows:

1. Identify the equation that must be used.
2. Since this problem involves continuous compound interest, you can use the respective equation, which is "A = Pe^rt."
3. A = Final amount
4. P = Initial amount
5. r = Interest rate
6. t = time
7. Identify the significance of the known information.
8. What is A, the final amount? That is $14,000.
9. What is P, the initial amount? This is what you are solving for and is still unknown.
10. Note: You will want to isolate this variable somehow.
11. What is r, the interest rate? That is 0.08.
12. What is t, the time (in years)? That is 4.
13. Substitute values into the equation.
14. You should yield the following equation: 14000 = Pe^0.08(4)
15. Isolate P, the unknown value.
16. This is simple, as you simply need to divide 14000 by e^0.08(4).
17. Your final answer should be $10,166.09.