Find the value after five years of a $3,000 savings account that pays 3% interest compounded yearly. Round the answer to two decimal places

Answer 1

To calculate the future value of a savings account with compound interest, you can use the formula:

$$A=P(1+r{)}^n$$

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:

• $P=3000$
• $r=0.03$ (3% expressed as a decimal)
• $n=5$

Now, plug the values into the formula:

$$A=3000(1+0.03{)}^5$$

First, calculate $1+0.03$:

$$1+0.03=1.03$$

Now raise $1.03$ to the power of 5:

$${1.03}^5\approx 1.159274$$

Next, multiply this by the principal $P$:

$$A=3000\times 1.159274\approx 3477.82$$

Finally, rounding to two decimal places, the value after five years will be:

$$\boxed{{\displaystyle 3477.82}}$$