How much money does D'Wayne need to deposit today to have $60,000 in 15 years if his account earns 4% compounded annually?

How much money does D'Wayne need to deposit today to have $60,000 in 15 years if his account earns 4% compounded annually?

• A. $60,000
• B. $33,316
• C. $40,000
• D. $50,000

Answer: (B)

To determine how much D'Wayne needs to deposit today in order to achieve a future goal of $60,000 in 15 years with an account earning 4% interest compounded annually, we can use the formula for present value: \[ PV = \frac{FV}{(1 + r)^n} \] Where: - \( PV \) is the present value (the amount to be deposited today). - \( FV \) is the future value ($60,000). - \( r \) is the annual interest rate (4%, or 0.04). - \( n \) is the number of years (15 years). By substituting the values into the formula, we have: \[ PV = \frac{60,000}{(1 + 0.04)^{15}} \] Calculating the denominator: \[ (1 + 0.04)^{15} = (1.04)^{15} \approx 1.8009 \] Now, substituting this value back into the present value calculation gives us: \[ PV = \frac{60,000}{1.8009} \approx 33,316.46 \] Therefore,

To determine how much D'Wayne needs to deposit today in order to achieve a future goal of $60,000 in 15 years with an account earning 4% interest compounded annually, we can use the formula for present value:

[

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

]

Where:

• ( PV ) is the present value (the amount to be deposited today).

• ( FV ) is the future value ($60,000).

• ( r ) is the annual interest rate (4%, or 0.04).

• ( n ) is the number of years (15 years).

By substituting the values into the formula, we have:

[

PV = \frac{60,000}{(1 + 0.04)^{15}}

]

Calculating the denominator:

[

(1 + 0.04)^{15} = (1.04)^{15} \approx 1.8009

]

Now, substituting this value back into the present value calculation gives us:

[

PV = \frac{60,000}{1.8009} \approx 33,316.46

]

Therefore,