What amount must be put in the bank today to achieve $1,000 in three years at an 8% interest rate using the discount method?

To determine the amount that must be deposited today to achieve a future value of $1,000 in three years at an 8% interest rate using the discount method, we use the present value formula. This formula is derived from the principle of the time value of money, which states that money available now is worth more than the same amount in the future due to its potential earning capacity.

The present value (PV) can be calculated using the formula:

[

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

]

Where:

• (FV) is the future value ($1,000 in this case),

• (r) is the interest rate (8%, or 0.08), and

• (n) is the number of years until the future value is realized (3 years).

Substituting in the values:

[

PV = \frac{1000}{(1 + 0.08)^3}

]

Calculating ( (1 + 0.08)^3 ):

[

(1.08)^3 \approx 1.259712

]

Now substituting back into the present value formula:

[

PV = \frac{1000}{1