To calculate the amount of money Lakisha would need to put into an account earning 5% interest compounded annually to reach $30,000 at the end of 20 years, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Where:
- A is the desired final amount ($30,000)
- P is the principal amount (initial deposit we want to find)
- r is the interest rate (as a decimal, 5% is 0.05)
- n is the number of compounding periods per year (1 for annually)
- t is the time in years (20 years)
Plugging in these values into the formula:
$30,000 = P(1 + 0.05/1)^(1*20)
Simplifying the equation:
$30,000 = P(1.05)^20
To find the principal amount (P), we divide both sides of the equation by (1.05)^20:
P = $30,000 / (1.05)^20
Using a calculator or a spreadsheet, we can evaluate this expression:
P ≈ $12,414
Therefore, Lakisha would need to put approximately $12,414 into the account to have $30,000 at the end of 20 years, when earning a 5% interest rate compounded annually.