Final answer:
John's $800 investment in an account with 8% interest compounded daily is worth approximately $1,790.85 after 10 years.
Step-by-step explanation:
When John invests $800 in an account that earns 8% interest compounded daily, we can calculate the future value of this investment over 10 years using the formula for compound interest:
A = P(1 + r/n)nt
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 times that interest is compounded per year.
- t is the time the money is invested for in years.
Given that the interest is compounded daily, n will be 365 (the number of days in a year) and t is 10 years. The annual interest rate of 8% should be converted to decimal form (r = 0.08). Plugging the values into the formula, we get:
A = 800(1 + 0.08/365)365×10
= $1,790.85
This calculation shows that after 10 years, John's account would be worth approximately $1,790.85.
Understanding the power of compound interest is critical for anyone interested in investments and savings. Starting to save money early and allowing it to grow through compounding can significantly increase the original investment over time.