A firm of attorneys deposit $5000 of profit sharing money at the end of each semi-annual period for 7.5 years. Find the final amount in the account in the account if the deposits earn 10% compounded semiannually. Find the amount of interest earned.
To find the final amount of money in the account, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount in the account
P = Principal amount (initial deposit)
r = Annual interest rate (as a decimal)
n = Number of compounding periods per year
t = Number of years
In this case:
P = $5,000 (profit sharing deposit at the end of each semi-annual period)
r = 10% = 0.10 (annual interest rate)
n = 2 (compounded semiannually)
t = 7.5 years
Using the compound interest formula, we can calculate the final amount:
A = 5000(1 + 0.10/2)^(2*7.5)
A = 5000(1 + 0.05)^(15)
A = 5000(1.05)^(15)
A ≈ $13,541.56
Therefore, the final amount in the account after 7.5 years will be approximately $13,541.56.
To find the amount of interest earned, subtract the principal amount from the final amount:
Interest = Final amount - Principal amount
Interest = $13,541.56 - $5,000
Interest ≈ $8,541.56
Therefore, the amount of interest earned over 7.5 years will be approximately $8,541.56.