When you retire 45 years from now, you want to have $1.25 million saved. You think you can earn an average of 7.6 percent, compounded annually, on your investments. To meet your goal, you are trying to decide whether to deposit a lump sum today, or to wait and deposit a lump sum five years from today to fund this goal. How much more will you have to deposit if you wait for five years before making the deposit?


Multiple Choice

$19,891.11


$20,468.85


$17,414.14


$21,319.47


$13,406.78

To determine how much more you'll have to deposit if you wait for five years, we can solve the problem using the future value formula for compound interest:

\[
FV = PV \times (1 + r)^t
\]

Where:
- $FV$ is the future value (in this case, \$1.25 million),
- $PV$ is the present value (the lump sum we need to calculate),
- $r$ is the annual interest rate (7.6% or 0.076),
- $t$ is the number of years.

### Step 1: Calculate the present value if deposited today.
The time period for depositing today is 45 years. We'll rearrange the formula to solve for $PV$:

\[
PV = \frac{FV}{(1 + r)^t}
\]

Substituting the values:

\[
PV = \frac{1,250,000}{(1 + 0.076)^{45}}
\]

### Step 2: Calculate the present value if deposited five years from now.
The time period if you wait for five years is 40 years (45 - 5). Using the same formula:

\[
PV_{\text{5 years}} = \frac{1,250,000}{(1 + 0.076)^{40}}
\]

### Step 3: Find the difference between the two amounts.
The difference is the extra amount you'll need to deposit if you wait for five years.

Let's calculate it.The difference between the two deposit amounts is approximately \$20,468.85. Therefore, if you wait five years before making the deposit, you will need to deposit \$20,468.85 more.

The correct answer is:

**\$20,468.85**

Would you like more details or have any further questions?

Here are five related questions to consider:
1. How is compound interest different from simple interest in savings calculations?
2. What is the impact of compounding frequency on your investment growth?
3. How would the required deposit change if the interest rate were lower?
4. What would happen to the future value if the interest was compounded monthly instead of annually?
5. How do inflation and real interest rates affect long-term savings goals?

**Tip:** Starting earlier with investments allows your money to grow more due to compound interest, reducing the required initial deposit.

When you retire 45 years from now, you want to have $1.25 million saved. You think you can earn an average of 7.6 percent, compounded annually, on your investments. To meet your goal, you are trying to decide whether to deposit a lump sum today, or to wait and deposit a lump sum five years from today to fund this goal. How much more will you have to deposit if you wait for five years before making the deposit?

Find out how much more you'll need to deposit if you wait five years before saving for retirement, aiming for $1.25 million in 45 years with a 7.6% annual return. Learn the compound interest formula and key concepts to calculate the difference in deposit amounts.

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