To calculate the balance of an account after a certain period of time with compound interest, we can use the formula:
A = P(1 + r/n)^(nt)
where A is the balance, P is the principal (initial investment), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time (in years).
Using this formula, we can calculate the balance in each of the accounts:
1. $10,000 invested at an APR of 4% for 10 years:
A = 10,000(1 + 0.04/1)^(1*10) = $14,802.44
2. $10,000 invested at an APR of 2.5% for 20 years:
A = 10,000(1 + 0.025/1)^(1*20) = $14,487.12
3. $15,000 invested at an APR of 3.2% for 25 years:
A = 15,000(1 + 0.032/1)^(1*25) = $38,210.10
4. $40,000 invested at an APR of 2.8% for 30 years:
A = 40,000(1 + 0.028/1)^(1*30) = $103,979.53
For compounding more than once a year, we can use the formula:
A = P(1 + r/n)^(nt)
where A is the balance, P is the principal (initial investment), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time (in years).
Using this formula, we can calculate the balance in each of the accounts:
1. $10,000 invested for 10 years with an APR of 2% and quarterly compounding:
A = 10,000(1 + 0.02/4)^(4*10) = $12,191.89
2. $2,000 invested for 5 years with an APR of 3% and daily compounding:
A = 2,000(1 + 0.03/365)^(365*5) = $2,319.81
3. $2,000 invested for 15 years with an APR of 5% and monthly compounding:
A