Suppose you want to have $700,000 for retirement in 35 years. Your account earns 4% interest.

a) How much would you need to deposit in the account each month?

$Incorrect

b) How much interest will you earn?

To solve this problem, we need to use the formula for the **future value of an ordinary annuity** since you're making regular deposits into an account that earns interest. The formula is:

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

Where:
- $FV$ is the future value (the amount you want to have in the account, $700,000),
- $P$ is the monthly deposit (which we want to find),
- $r$ is the annual interest rate (4%, or 0.04),
- $n$ is the number of times the interest is compounded per year (monthly means $n = 12$),
- $t$ is the time in years (35 years).

### Part a) Finding the monthly deposit $P$

We need to rearrange the formula to solve for $P$:

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

Let’s substitute the given values into the equation:
- $FV = 700,000$,
- $r = 0.04$,
- $n = 12$,
- $t = 35$.

Now, let's calculate $P$.

The monthly deposit $P$ you would need to make is approximately **$766.09**.

### Part b) How much interest will you earn?

To find the total interest earned, we need to first calculate the total amount deposited over the 35 years, and then subtract that from the future value.

The total amount deposited is:

\[
\text{Total Deposits} = P \times n \times t
\]

The interest earned is:

\[
\text{Interest} = FV - \text{Total Deposits}
\]

Let's compute this next.The total amount you will deposit over 35 years is approximately **$321,757.74**.

The interest you will earn is approximately **$378,242.26**.

Would you like more details or have any questions about the solution?

Here are 5 related questions to further explore:
1. What would the monthly deposit be if the interest rate were 5% instead of 4%?
2. How much more would you earn in interest if the savings period were 40 years instead of 35?
3. What would happen to the required monthly deposit if you wanted to save $1,000,000 instead of $700,000?
4. How would the monthly deposit change if the interest were compounded quarterly instead of monthly?
5. What is the impact of delaying the start of deposits by 5 years?

**Tip:** The earlier you start saving for long-term goals, the more you benefit from compound interest. Even small monthly deposits can grow significantly over time.

Suppose you want to have $700,000 for retirement in 35 years. Your account earns 4% interest. a) How much would you need to deposit in the account each month? b) How much interest will you earn?

Learn how to calculate the monthly deposit needed to save $700,000 for retirement in 35 years with a 4% interest rate. Discover how much interest you'll earn using the future value of annuities and compound interest formulas.

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