You want to have $$ \$ 400,000 $$ when you retire in 25 years. If you can earn $$ 5 \% $$ interest compounded weekly, how much would you need to deposit now into the account to reach your retirement goal?

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To determine how much you need to deposit now to reach your retirement goal of $$ \$400,000 $$ in 25 years with an interest rate of $$ 5\% $$ compounded weekly, we can use the formula for the present value of a future sum:

$$
PV = \frac{FV}{(1 + r/n)^{nt}}
$$

Where:
- $$ PV $$ is the present value (the amount to deposit now),
- $$ FV $$ is the future value (the amount desired in the future, which is $$ \$400,000 $$),
- $$ r $$ is the annual interest rate (as a decimal, so $$ 0.05 $$),
- $$ n $$ is the number of times interest is compounded per year (for weekly compounding, $$ n = 52 $$),
- $$ t $$ is the number of years until the amount is needed (which is $$ 25 $$).

Now, we can plug in the values:

- $$ FV = 400,000 $$
- $$ r = 0.05 $$
- $$ n = 52 $$
- $$ t = 25 $$

First, we calculate $$ r/n $$:

$$
r/n = \frac{0.05}{52} \approx 0.0009615385
$$

Next, we calculate $$ nt $$:

$$
nt = 52 \times 25 = 1300
$$

Now we can substitute these values into the present value formula:

$$
PV = \frac{400,000}{(1 + 0.0009615385)^{1300}}
$$

Calculating $$ (1 + 0.0009615385)^{1300} $$:

$$
(1 + 0.0009615385)^{1300} \approx (1.0009615385)^{1300} \approx 4.386
$$

Now we can calculate $$ PV $$:

$$
PV = \frac{400,000}{4.386} \approx 91,155.36
$$

Thus, the amount you need to deposit now to reach your retirement goal of $$ \$400,000 $$ in 25 years is approximately:

$$
\boxed{91,155.36}
$$
To reach a retirement goal of $$ \$400,000 $$ in 25 years with a $$ 5\% $$ weekly compounded interest, you would need to deposit approximately $$ \$91,155.36 $$ now.

You want to have when you retire in 25 years. If you can earn interest compounded weekly,
how much would you need to deposit now into the account to reach your retirement goal?

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You want to have when you retire in 25 years. If you can earn interest compounded weekly, how much would you need to deposit now into the account to reach your retirement goal?