Find the balance after 10 years of a $30,000 savings account that pays 10% interest compounded yearly.(1 point) Responses

Answer 1

To calculate the balance of a savings account with compounded interest, you 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:

• $P=30,000$
• $r=0.10$ (10%)
• $n=10$

Substituting the values into the formula:

$$A=30000(1+0.10{)}^{10}$$

$$A=30000(1.10{)}^{10}$$

Calculating $(1.10{)}^{10}$:

$$(1.10{)}^{10}\approx 2.59374$$

Now, multiply this by the principal:

$$A\approx 30000\times 2.59374\approx 77712.20$$

Thus, the balance after 10 years will be approximately $77,712.20.