Question

On the day of a child's birth, a parent deposits 30,000 dollar in a trust fund that pays $5 \%$ interest, compounded continuously. Determine the balance in this account on the child's 25 th birthday.

Name: Problem 63, Chapter 3: Precalculus
Uploaded: 2023-07-21T15:14:05-08:00
Duration: 1 min 47 s
Channel: Courtney R
Description: On the day of a child's birth, a parent deposits 30,000 dollar in a trust fund that pays 5 % interest, compounded continuously. Determine the balance in this account on the child's 25 th birthday.

   On the day of a child's birth, a parent deposits 30,000 dollar in a trust fund that pays $5 \%$ interest, compounded continuously. Determine the balance in this account on the child's 25 th birthday.

Precalculus

Ron Larson 9th Edition

Chapter 3, Problem 63

Instant Answer

Solved by Expert Courtney R

07/21/2023

Step 1

The formula to calculate the future value of an investment with continuous compounding is given by: \[ A = Pe^{rt} \] where: $ A $ = the amount of money accumulated after n years, including interest. $ P $ = the principal amount (initial deposit). \( Show more…

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On the day of a child's birth, a parent deposits 30,000 dollar in a trust fund that pays $5 \%$ interest, compounded continuously. Determine the balance in this account on the child's 25 th birthday.

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Key Concepts

Compound Interest

Compound interest refers to the process where interest is added to the principal so that, from that moment on, the interest that has been added also earns interest. This results in exponential growth over time as interest is calculated on the accumulated total rather than solely on the initial deposit.

Continuous Compounding

Continuous compounding is a concept in finance where interest is theoretically added to the principal an infinite number of times per period, leading to a smooth, exponential growth pattern. This is modeled mathematically with the formula A = Pe^(rt), where e is the base of the natural logarithm.

Exponential Growth

Exponential growth describes a process where a quantity increases at a rate proportional to its current value. In the context of finance, applying the exponential function to continuous compounding highlights how investments grow more rapidly as the accrued interest itself earns additional returns over time.

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