Final answer:
The balance after t years with continuous compounding interest is found using the formula A(t) = Pe^{rt}, where P is the principal amount, r is the interest rate, and t is the time in years. For a $4000 deposit at 3.5% interest, the formula is A(t) = 4000e^{0.035t}.
Step-by-step explanation:
When a student deposits money into a savings account with continuous compounding interest, the formula to calculate the balance after t years, A(t), is given by the equation A(t) = Pert. In this case, the principal amount P is $4000, the rate r is 3.5% or 0.035, and t represents the time in years. Therefore, the formula becomes A(t) = 4000e0.035t.
Compound interest, as opposed to simple interest, capitalizes on both the principal and the accumulated interest, resulting in a faster growth of your investment over time. This is clearly demonstrated in cases similar to the one presented in Box 1.2 and in the scenario where $3000 grows fifteen fold over 40 years with a 7% return.