Final answer:
Lolita will have approximately $1,039.46 in her savings account after 15 years with a 5% annual compound interest rate. The correct answer is D) approximately $1,000, as it is closest to the calculated amount.
Step-by-step explanation:
Calculating Compound Interest for Lolita's Savings
To calculate how much money Lolita will have in her savings account after 15 years with a 5% compounded annual interest rate, we can use the compound interest formula:
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.
In Lolita's case, we have:
- P = $500
- r = 0.05 (5% as a decimal)
- n = 1 (because it is compounded annually)
- t = 15 years
Plugging these values into the formula gives us:
A = 500(1 + 0.05/1)^(1*15)
A = 500(1 + 0.05)^15
A = 500(1.05)^15
A = 500 * 2.07893
A ≈ $1,039.46
Therefore, Lolita will have approximately $1,039.46 in her account 15 years from now, which means that option A) Lolita will have approximately $894.62 in her account 15 years from now is not the correct answer. We performed the calculation and reached a value close to $1,000, but due to the effect of compound interest over 15 years, the amount is slightly higher than $1,000, ruling out options B) and C) as well. Hence, the closest correct answer among the options provided is D) Lolita will have approximately $1,000 in her account 15 years from now.