You want to have 5,000 in a savings account after 3 years, and the account earns 6% interest compounded annually. How much should you initially deposit to achieve this goal?

To solve this problem, you can use the formula for compound interest, which is:

A = P (1 + r/n)^(nt)

Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = the time the money is invested for in years

In this case, you want to find out the initial deposit (P), so you need to rearrange the formula to solve for P:

P = A / (1 + r/n)^(nt)

You know that A = $5,000, r = 6% or 0.06 (in decimal), n = 1 (since the interest is compounded annually), and t = 3 years.

Substitute these values into the formula:

P = 5000 / (1 + 0.06/1)^(1*3) P = 5000 / (1.06)^3 P = 5000 / 1.191016 P = $4,199.57

So, you should initially deposit approximately $4,199.57 to achieve your goal of having$5,000 in a savings account after 3 years with an annual interest rate of 6% compounded annually.