Final answer:
Lakisha would need to invest $11,306 at an annual compound interest rate of 5% to have $30,000 in 20 years. Compound interest is better than simple interest because it allows the interest to earn interest, resulting in a faster growth of the investment over time.
Step-by-step explanation:
To determine how much money Lakisha would need to invest today to have $30,000 at the end of 20 years with an annual compound interest rate of 5%, we use the formula for compound interest, which is:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
Here, Lakisha wants $30,000 after 20 years, and the interest rate is 5% compounded annually (n=1). We rearrange the formula to solve for P:
P = A / (1 + r/n)^(nt)
Substituting the known values:
P = $30,000 / (1 + 0.05/1)^(1*20)
P = $30,000 / (1.05)^20
P = $30,000 / 2.6533
P = $11,305.54
To the nearest dollar, Lakisha needs to invest $11,306.