Final answer:
To find out how much Rita will have after 5 years by investing $3,500 at 6% interest compounded monthly, we use the compound interest formula A = P(1 + r/n)^(nt). Substituting in the values, we calculate that Rita will have approximately $4,700.71. This total includes her initial investment plus the interest accrued.
Step-by-step explanation:
Calculating Compound Interest for College Tuition Savings
Rita inherited $3,500 and plans to invest this amount for college tuition in an account offering 6% interest compounded monthly. To determine how much money she will have after 5 years, 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.
Using the values provided:
- P = $3,500
- r = 6% or 0.06 (as a decimal)
- n = 12 (since interest is compounded monthly)
- t = 5 years
Now, plug in the values into the formula:
A = 3500(1 + 0.06/12)12*5
Calculating the value inside the parentheses first and then raising it to the power of 60 (12 months * 5 years), we get:
A ≈ $4,700.71
Thus, after 5 years, Rita will have approximately $4,700.71 in her account, which is the sum of her initial investment and the interest accrued over time thanks to the power of compound interest.