Final answer:
To calculate the balance with different compounding periods on a $5000 investment at 5% interest, we use the compound interest formula. Annually compounded, the balance after one year is $5250. More frequent compounding quarterly, monthly, and daily results in slightly higher balances due to more frequent application of interest.
Step-by-step explanation:
To determine the balance of a $5000 investment earning 5% interest compounded annually, quarterly, monthly, and daily, we use the compound interest formula A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for.
Annually: Compounded once per year (n = 1), the formula becomes A = $5000(1 + 0.05/1)^(1*t). Assuming the investment is for one year, the balance would be $5250.
Quarterly: Compounded four times per year (n = 4), the balance after one year is calculated as A = $5000(1 + 0.05/4)^(4*t), resulting in a balance of $5263.19.
Monthly: For monthly compounding (n = 12), we would find A = $5000(1 + 0.05/12)^(12*t), which would yield a balance of $5271.14 after one year.
Daily: If compounded daily (n = 365), the balance after one year would be A = $5000(1 + 0.05/365)^(365*t), and the final amount would be $5275.63.
These calculations show how more frequent compounding increases the total amount of interest earned on the principal investment.