Question

Alice is opening a savings account that earns 2.2% interest, compounded continuously. How much will she need to deposit in the account so that she has $6200 after 3 years?

A) $5,500
B) $5,600
C) $5,700
D) $5,804

Answer 1

Alice needs to deposit approximately $5804 in her savings account with continuous compounding at a rate of 2.2% to achieve $6200 after 3 years, corresponding to option D).

Step-by-step explanation:

To find out how much Alice needs to deposit in her savings account with a 2.2% interest rate, compounded continuously, so that she has $6200 after 3 years, we use the formula for continuous compounding:

A = Pert

Where A is the future value of the investment/loan, including interest, P is the principal investment amount (initial deposit), r is the annual interest rate (decimal), t is the time the money is invested for, in years, and e is the base of the natural logarithm.

We know that A = $6200, r = 0.022, and t = 3. We need to find P.

Therefore, we rearrange the formula to solve for P:

P = A / ert

P = $6200 / e(0.022)(3)

Calculating the right-hand side, we find:

P = $6200 / e0.066

P = $6200 / 1.0682≈

P ≈ $5803.55

So, Alice would need to deposit approximately $5804 to reach her goal, which corresponds to option D).