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galina1969
10 days ago
12

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.
Mathematics
1 answer:
PIT_PIT [9.1K]10 days ago
3 0

Response:

To accumulate $7,500 in three years, the required one-time deposit is $4388.17

Step-by-step explanation:

Basic Financial Formulas

A commonly used formula for calculating present and future values is

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

Where FV represents the future value, PV denotes the present value, r signifies the interest rate, and n indicates the number of compounding periods. It’s essential to remember that r and n must correspond to the same compounding duration, e.g. r is compounded monthly while n is expressed in months.

The inquiry seeks to determine the PV necessary as a one-time deposit to achieve a future value of $7,500 in 3 years at an interest rate of 1.5% compounded monthly.

FV=7,500

r=1.5%=0.015

n=3*12=36 months

We have changed n to months since r is monthly compounded. The equation

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

must be arranged to isolate PV.

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

PV=7,500(1+0.015)^{-36}

PV=\$4388.17

Response

: The amount necessary as a one-time deposit to accrue $7,500 in three years is $4388.17[[TAG_54]]
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