Question

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?

Answer 1

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

Answer 2

$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.