Question
Andy has $100 in an account. The interest rate is 6% compounded annually. To the nearest cent, how much will he have in 2 years?
Answers
GPT-4o mini
To find out how much Andy will have in his account after 2 years with an initial amount of $100, an interest rate of 6%, and compounded annually, we can use the formula for compound interest:
\[
A = P(1 + r)^n
\]
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 years the money is invested or borrowed.
In this case:
- \(P = 100\)
- \(r = 0.06\)
- \(n = 2\)
Now substituting the values into the formula:
\[
A = 100(1 + 0.06)^2
\]
Calculating inside the parentheses first:
\[
1 + 0.06 = 1.06
\]
Now raise \(1.06\) to the power of 2:
\[
1.06^2 = 1.1236
\]
Now multiply by the principal amount:
\[
A = 100 \times 1.1236 = 112.36
\]
Therefore, after 2 years, Andy will have **$112.36** in his account.
\[
A = P(1 + r)^n
\]
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 years the money is invested or borrowed.
In this case:
- \(P = 100\)
- \(r = 0.06\)
- \(n = 2\)
Now substituting the values into the formula:
\[
A = 100(1 + 0.06)^2
\]
Calculating inside the parentheses first:
\[
1 + 0.06 = 1.06
\]
Now raise \(1.06\) to the power of 2:
\[
1.06^2 = 1.1236
\]
Now multiply by the principal amount:
\[
A = 100 \times 1.1236 = 112.36
\]
Therefore, after 2 years, Andy will have **$112.36** in his account.