Questions: You deposit 3000 in an account earning 8% interest compounded monthly. How much will you have in the account in 10 years?

Transcript text: You deposit $\$ 3000$ in an account earning $8 \%$ interest compounded monthly. How much will you have in the account in 10 years? $\$$

Solution

Solution Steps

Step 1: Understanding the Problem

We are given an initial deposit (Principal) $P$, an annual interest rate $r\%$, and the time $t$ years for which the money is invested. The interest is compounded monthly.

Step 2: Applying the Future Value Formula

The future value $FV$ can be calculated using the formula: \[FV = P \left(1 + \frac{r}{100 \cdot n}\right)^{n \cdot t}\] where:

$P$ is the initial deposit amount (Principal),
$r$ is the annual interest rate in percentage,
$n=12$ is the number of times the interest is compounded per year (monthly compounding),
$t$ is the time the money is invested or borrowed for, in years.

Step 3: Plugging in the Given Values

Given: $P = 3000$, $r = 8\%$, $t = 10$ years, and $n = 12$ (monthly compounding). We calculate the future value as follows: \[FV = 3000 \left(1 + \frac{8}{100 \cdot 12}\right)^{12 \cdot 10}\]