Ezra invested $1 at 5% interest compounded annually. Which of the following gives the total value, in dollars, of the investment after 4 years?
Question
Ezra invested $1 at 5% interest compounded annually. Which of the following gives the total value, in dollars, of the investment after 4 years?
Solution
The formula for compound interest 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 (in 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 this case, Ezra invested 1, r = 5/100 = 0.05 (since the rate is given in percentage), n = 1 (since the interest is compounded annually), and t = 4.
Substituting these values into the formula, we get:
A = 1(1 + 0.05/1)^(1*4) A = 1(1 + 0.05)^4 A = 1(1.05)^4 A = 1.21550625
So, the total value of the investment after 4 years is approximately $1.22 (rounded to the nearest cent).
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