Question
Tyrone and Regan deposit $1,000.00 into a savings account which earns 2% interest compounded annually. They want to use the money in the account to go on a trip in 3 years. How much will they be able to spend?
Round your answer to the nearest cent.
Round your answer to the nearest cent.
Answers
GPT-4o mini
To calculate how much Tyrone and Regan will have in their savings account after 3 years with an annual interest rate of 2% 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, which is $1,000.00).
- \( r \) is the annual interest rate (decimal) (2% = 0.02).
- \( n \) is the number of years the money is invested or borrowed (3 years).
Plugging in the values:
\[
A = 1000(1 + 0.02)^3
\]
Now, calculate \( (1 + 0.02) \):
\[
1 + 0.02 = 1.02
\]
Now raise this to the power of 3:
\[
(1.02)^3 \approx 1.061208
\]
Now multiply this by the principal \( P = 1000 \):
\[
A \approx 1000 \times 1.061208 \approx 1061.21
\]
Thus, the total amount they will have after 3 years is approximately **$1,061.21**.
Therefore, they will be able to spend **$1,061.21** for their trip.
\[
A = P(1 + r)^n
\]
where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money, which is $1,000.00).
- \( r \) is the annual interest rate (decimal) (2% = 0.02).
- \( n \) is the number of years the money is invested or borrowed (3 years).
Plugging in the values:
\[
A = 1000(1 + 0.02)^3
\]
Now, calculate \( (1 + 0.02) \):
\[
1 + 0.02 = 1.02
\]
Now raise this to the power of 3:
\[
(1.02)^3 \approx 1.061208
\]
Now multiply this by the principal \( P = 1000 \):
\[
A \approx 1000 \times 1.061208 \approx 1061.21
\]
Thus, the total amount they will have after 3 years is approximately **$1,061.21**.
Therefore, they will be able to spend **$1,061.21** for their trip.