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Mrs. Ryan put $5,000 into a college fund when James turned 3 years old. The fund increases at a 4% interest rate compounded annually. No other deposits or withdrawals were made. What is the approximate amount of money in James' account when he turns 18 years old?

2 Answers

1 vote

Answer: The approximate amount of money in James' account when he turns 18 years old is approximately $8,749.00.

Explanation:

To calculate the approximate amount of money in James' account when he turns 18 years old, we can use the formula for compound interest:

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

Where:

A = the final amount of money in the account

P = the initial principal (deposit) amount

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, Mrs. Ryan initially deposited $5,000 into the account, the interest rate is 4% (or 0.04 as a decimal), and the interest is compounded annually (n = 1). The time period is 15 years since James turns 18 and the initial deposit was made when he was 3 (18 - 3 = 15).

Plugging the values into the formula:

A = 5000(1 + 0.04/1)^(1*15)

A = 5000(1.04)^15

A ≈ 5000(1.7498)

A ≈ $8,749.00

Thereforec

User MrOrhan
by
7.3k points
6 votes

Answer:

$8,749

Explanation:

Compound Interest


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

where:

  • A is the amount of money at the end of the investment period
  • P is the principal amount (the initial investment)
  • r is the annual interest rate (as a decimal)
  • n is the number of times the interest is compounded per year
  • t is the time (in years) of the investment period

Given:

  • P = $5,000
  • r = 0.04 (4% expressed as a decimal)
  • n = 1 (compounded annually)
  • t = 15 (the time from when James was 3 years old to when he turns 18)

Substitute the given values into the formula:


\implies A = \$5,000(1 + (0.04)/(1))^((1\cdot 15))


\implies A = \$5,000(1.04)^(15)


\implies A \approx \$8,749


\therefore The approximate amount of money in James' account when he turns 18 years old is $8,749.

User Yarg
by
8.9k points

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