Question

When+Martin+was+born+his+father+set+up+a+5,000+college+fund+for+him+with+an+annual+compound+interest+rate+of+7.5 What+is+the+total+value+of+this+account+after+18+years+and+what+was+the+interest+earned+on+the+account+Round+the+answers+to+two+decimal+places.
The final amount of the college fund is $( ) and the amount of
interest+earned+on+the+account+is+( )

Answers

GPT-4o mini
To find the total value of the college fund after 18 years with an initial investment of $5,000, an annual compound interest rate of 7.5%, we can use the formula for compound interest:

\[
A = P(1 + r)^n
\]

Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of years the money is invested or borrowed.

Given:
- \( P = 5000 \)
- \( r = 7.5\% = 0.075 \)
- \( n = 18 \)

Now, substituting the values into the formula:

\[
A = 5000(1 + 0.075)^{18}
\]

Calculating \( (1 + 0.075) \):

\[
1 + 0.075 = 1.075
\]

Next, calculate \( (1.075)^{18} \):

\[
(1.075)^{18} \approx 3.703
\]

Now, substitute this value back into the equation:

\[
A = 5000 \times 3.703 \approx 18515.00
\]

Now we can calculate the interest earned:

\[
\text{Interest Earned} = A - P = 18515.00 - 5000 = 13515.00
\]

So, the total value of the college fund is approximately $18,515.00, and the interest earned is approximately $13,515.00.

The final answers are:
- The final amount of the college fund is $(18515.00)$ and the amount of interest earned on the account is $(13515.00)$.