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How much money, as a one-time deposit, PV, would you need to deposit into an account that earns 1.5% compounded monthly to earn a future value, FV, of $7,500 in three years? This amount can be found by using algebra to rearrange the function, FV=PV(1+rn)(nY), so that FV becomes an input variable and PV becomes the output variable. PV=FV(1+rn)(−nY) Use this function to find the amount needed as a one-time deposit to earn $7,500 in 3 years.

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elcharly64

Answer:

The amount needed as a one-time deposit to earn $7,500 in 3 years is $4388.17

Step-by-step explanation:

Basic Finance Formulas

One of the most-used formulas to compute present and future values is

[tex]FV=PV(1+r)^{n}[/tex]

Where FV is the future value, PV is the present value, r is the interest rate and n is the number of periods. It's vital to keep in mind that r and n must be referred to the same compounded time, e.g. r is compounded monthly and n is expressed in months

The question requires to compute the PV needed as a one-time deposit to earn a future value of $7,500 in 3 years at a 1.5% rate compounded monthly.

FV=7,500

r=1.5%=0.015

n=3*12=36 months

We converted n to months because r is compounded monthly . The formula

[tex]FV=PV(1+r)^{n}[/tex]

must be managed to make PV isolated

[tex]PV=FV(1+r)^{-n}[/tex]

[tex]PV=7,500(1+0.015)^{-36}[/tex]

[tex]PV=\$4388.17[/tex]

Answer: The amount needed as a one-time deposit to earn $7,500 in 3 years is $4388.17

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