 You deposit $200 every three months into an account earning 7% interest compounded quarterly.
How much will you have in the account in 25 years?



To solve this, we need to apply the formula for the **future value of an ordinary annuity** where regular payments are made into an account that earns compound interest. The formula is:

\[
FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)
\]

Where:
- $FV$ = future value of the annuity (the amount in the account after 25 years)
- $P$ = regular deposit ($200)
- $r$ = interest rate per period (quarterly rate, which is 7% annual compounded quarterly, so $ r = \frac{7\%}{4} = 0.0175 $)
- $n$ = total number of periods (25 years $ \times $ 4 quarters per year = 100)

Now let's plug in the values:

\[
FV = 200 \times \left( \frac{(1 + 0.0175)^{100} - 1}{0.0175} \right)
\]

I'll calculate this.

You deposit $200 every three months into an account earning 7% interest compounded quarterly. How much will you have in the account in 25 years?

Calculate the future value of $200 deposited every three months into an account earning 7% interest compounded quarterly over 25 years. This step-by-step solution explains the use of the future value of an ordinary annuity formula, covering key concepts in compound interest and time value of money.

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