Final answer:
The balance after 10 years of $10,000 invested at a 3.2% interest rate compounded monthly can be found using the compound interest formula A = P(1 + r/n)^(nt), with P as the principal, r as the annual interest rate, n as the number of compounding periods per year, and t as the time in years.
Step-by-step explanation:
To calculate the balance of $10,000 invested at a 3.2% interest rate compounded monthly after 10 years, we use the compound interest formula. The formula we use is A = P(1 + \(\frac{r}{n}\))^\(nt\), where:
- 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
In your case:
- P = $10,000
- r = 3.2% or 0.032 (as a decimal)
- n = 12 (since it is compounded monthly)
- t = 10 years
Now, plug these values into the formula to find A:
A = $10,000(1 + \(\frac{0.032}{12}\))^(12 \(\times\) 10)
Calculating this gives us a final balance after 10 years.
This compounded interest will result in a higher balance compared to simple interest, as it's calculated on the principal plus the accumulated interest. Over time, this can make a significant difference to the balance for larger sums of money and longer investment periods.