Find the balance in the account: $2,000 principal, earning 7% compounding
semi-annually, after 25 years.
To calculate the balance in the account after 25 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested/borrowed for
Given:
P = $2,000
r = 7% = 0.07
n = 2 (compounded semi-annually)
t = 25 years
Plugging in the values:
A = $2,000(1 + 0.07/2)^(2*25)
A = $2,000(1 + 0.035)^50
A = $2,000(1.035)^50
A = $2,000(2.6912)
A = $5,382.40
Therefore, the balance in the account after 25 years would be $5,382.40.
can you make it simpler
Sure! Here's a simpler way to calculate the balance:
1. Find the annual interest rate in decimal form: 7% = 0.07
2. Find the effective interest rate per compounding period (semi-annually): 0.07 / 2 = 0.035
3. Calculate the total number of compounding periods over 25 years: 2 compounding periods per year * 25 years = 50 periods
4. Use the formula for compound interest: A = P(1 + r/n)^(nt)
5. Plug in the values: A = $2,000(1 + 0.035)^50
6. Calculate: A = $2,000(1.035)^50 = $5,382.40
Therefore, the balance in the account after 25 years would be $5,382.40.