Math Problem Statement

Suppose that money is deposited daily into a savings account at an annual rate of $800. If the account pays 4% interest compounded continuously, estimate the balance in the account at the end of 3 years.

Solution

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Math Problem Analysis

Mathematical Concepts

Continuous Compounding
Continuous Deposits
Exponential Growth

Formulas

Continuous compound interest formula: A = Pe^(rt)
Integral for continuous deposits: S = ∫(P(t) * e^(r(T-t))) dt

Theorems

Exponential Growth Theorem

Suitable Grade Level

Undergraduate Level