To achieve a future value of $50,000 in 8 years at an interest rate of 5%, what is the nearest initial investment needed?

To achieve a future value of $50,000 in 8 years at an interest rate of 5%, what is the nearest initial investment needed?

• A. $18,536
• B. $33,842
• C. $19,633
• D. $32,898

Answer: (B)

To determine the nearest initial investment needed to achieve a future value of $50,000 in 8 years at an interest rate of 5%, we can use the formula for future value in terms of the present value (initial investment): \[ FV = PV \times (1 + r)^n \] Where: - \( FV \) is the future value, - \( PV \) is the present value (initial investment), - \( r \) is the interest rate (as a decimal), - \( n \) is the number of years. Rearranging this formula to solve for the present value gives: \[ PV = \frac{FV}{(1 + r)^n} \] In this case: - \( FV = 50,000 \) - \( r = 0.05 \) (5% as a decimal) - \( n = 8 \) Substituting these values into the equation: \[ PV = \frac{50,000}{(1 + 0.05)^8} \] Calculating \( (1 + 0.05)^8 \): \[ (1.05)^8 \approx 1.36049 \] Thus

To determine the nearest initial investment needed to achieve a future value of $50,000 in 8 years at an interest rate of 5%, we can use the formula for future value in terms of the present value (initial investment):

[

FV = PV \times (1 + r)^n

]

Where:

• ( FV ) is the future value,

• ( PV ) is the present value (initial investment),

• ( r ) is the interest rate (as a decimal),

• ( n ) is the number of years.

Rearranging this formula to solve for the present value gives:

[

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

]

In this case:

• ( FV = 50,000 )

• ( r = 0.05 ) (5% as a decimal)

• ( n = 8 )

Substituting these values into the equation:

[

PV = \frac{50,000}{(1 + 0.05)^8}

]

Calculating ( (1 + 0.05)^8 ):

[

(1.05)^8 \approx 1.36049

]

Thus