Compound Interest

Question

Diego deposited a certain sum of money in a bank 2 years ago. If the bank had been paying interest at the rate of 6% compounded continuously and he has $12,000 on deposit today, what was his initial deposit?

Answer 1

Hello, thank you for taking the time to post your question!

The underlying formula that you want to use here for continuous compounding is

A = P*e^(rt)

Based on the information given in the question we have

12000 = P * e^(0.06*2)

Solving that algebraically for “P” I get

P = 12000 / e^(0.06*2) = 10,643.05

Meaning that the initial deposit made was $10,643.05

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Continuous compound interest follows the formula:

A(t) = A₀ e^rt

 

Where A₀ is initial deposit, r is the interest rate, and t is the time. In your problem, you know that t=2, A(2) = 12,000, and r = 0.06. Plug these into your calculator, and you should be able to solve for A₀ fairly readily.

 

Hope this helps, and please comment if you have further questions!