How much must be set aside each year at a 6% interest rate to accumulate $18,000 in 6 years?

To determine how much needs to be set aside each year at a 6% interest rate to accumulate $18,000 in 6 years, we can use the future value of an annuity formula. This type of calculation is relevant when you're making regular deposits to grow a certain amount over time at a specified interest rate.

The formula for the future value of an annuity is:

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

Where:

• ( FV ) is the future value of the annuity (in this case, $18,000),

• ( P ) is the annual payment (the amount we want to find),

• ( r ) is the interest rate per period (6% or 0.06),

• ( n ) is the total number of payments (6 years).

Rearranging the formula to solve for ( P ):

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

Now substituting the known values:

[ P = \frac{18000 \cdot 0.06}{(1 + 0.06)^6 - 1} \