If Venus wants to have $30,000 in her taxable account at the end of 10 years with an annual return of 6%, how much does she need to invest per year?

To determine how much Venus needs to invest each year to reach her goal of $30,000 in a taxable account after 10 years with an annual return of 6%, we can use the future value of an annuity formula. This formula allows us to calculate how much to contribute annually to achieve a specified future value, accounting for compound interest.

The future value of an annuity formula is expressed as:

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

Where:

• ( FV ) is the future value ($30,000 in this case),

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

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

• ( n ) is the number of years (10 years in this case).

Rearranging this formula to solve for ( P ) gives:

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

Plugging in the values:

• ( FV = 30,000 )

• ( r = 0.06 )

• ( n = 10 )

The