Math Problem Statement

When Jason Levy was born, his grandparents deposited $1500 into a special account for Jason's college education. The account earned 3% interest, compounded daily. How much money will be in the account when Jason is 18?

Solution

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Problem:
When Jason Levy was born, his grandparents deposited $1500 into a special account for Jason's college education. The account earned 3% interest, compounded daily. How much money will be in the account when Jason is 18?

To solve this, we can apply the compound interest formula:

A=P(1+rn)ntA = P \left( 1 + \frac{r}{n} \right)^{nt}

Where:

  • AA is the amount of money in the account after tt years.
  • PP is the principal amount (initial deposit), which is $1500.
  • rr is the annual interest rate (decimal form), so 3% becomes 0.03.
  • nn is the number of times the interest is compounded per year. Since it's compounded daily, n=365n = 365.
  • tt is the number of years the money is invested or borrowed for, which is 18 years.

Let me calculate the amount of money in the account when Jason is 18. Given values for the problem P = 1500 # principal amount in dollars r = 0.03 # annual interest rate (3%) n = 365 # daily compounding t = 18 # years

Compound interest formula

A = P * (1 + r / n) ** (n * t) AThe amount of money in the account when Jason is 18 years old will be approximately $2573.95.

If you need any further details or explanations on the calculation, feel free to ask!

Related questions for deeper understanding:

  1. What is the effect of increasing the interest rate on the final amount?
  2. How does the number

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Math Problem Analysis

Mathematical Concepts

Compound Interest
Exponential Growth
Finance

Formulas

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

Theorems

Compound Interest Theorem

Suitable Grade Level

Grades 9-11