You deposit $390 every six months into an account earning 6.1% interest compounded semiannually.

a) How much will you have in the account in 20 years?

$


b) How much total money will you put into the account?

$


c) How much total interest will you earn?


This problem involves calculating the future value of an annuity with semiannual compounding interest. Let’s break it down step-by-step.

### Given information:
- **Deposit amount (PMT)** = $390
- **Interest rate (r)** = 6.1% annually (0.061 as a decimal)
- **Compounding frequency** = semiannually (twice a year)
- **Time period (t)** = 20 years

#### Adjustments for semiannual compounding:
- **Number of periods (n)** = $20 \text{ years} \times 2 = 40$ periods
- **Interest rate per period (i)** = $\frac{6.1\%}{2} = 3.05\% = 0.0305$ per period

### Part (a): Future Value of the Annuity

The future value $FV$ of an ordinary annuity (where deposits are made at the end of each period) is calculated by the formula:
\[
FV = PMT \times \frac{(1 + i)^n - 1}{i}
\]

Substitute in the values:
\[
FV = 390 \times \frac{(1 + 0.0305)^{40} - 1}{0.0305}
\]

1. Calculate $ (1 + 0.0305)^{40} $:
2. Subtract 1 from the result.
3. Divide by 0.0305.
4. Multiply by 390 to get $FV$.

Let’s calculate this step-by-step.

### Part (b): Total Money Deposited

Since deposits are made every six months for 20 years:
\[
\text{Total Deposits} = PMT \times n = 390 \times 40
\]

### Part (c): Total Interest Earned

The interest earned is the difference between the future value and the total deposits:
\[
\text{Interest Earned} = FV - \text{Total Deposits}
\]

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Let me calculate these values.

You deposit $390 every six months into an account earning 6.1% interest compounded semiannually.

 a) How much will you have in the account in 20 years?

 b) How much total money will you put into the account?

 c) How much total interest will you earn?

Learn how to calculate the future value of depositing $390 every six months into an account with 6.1% interest compounded semiannually. This example guides you through key financial concepts, including annuities and the time value of money. Suitable for high school students in Grades 10-12.

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