Lamar needs 2308 for a future project. He can invest 2000 now at an annual rate of , compounded semiannually. Assuming that no withdrawals are made, how long will it take for him to have enough money for his project

Find detailed explanation below

Explanation:

The required future amount of 2308 is the future value of the amount invested today, hence, using the future value formula as provided below, we can determine the length of time it takes Lamar to accumulate enough money for the project.

FV=PV*(1+r/n)^mn

FV=2308

PV=2000

r=4%(assumed in order to explain the concept of the time value of money in a clearer context)

n=2(interest is compounded semiannually, twice a year)

m=number of years it takes to accumulate enough money=unknown

2308=2000*(1+4%/2)^2*m

2308/2000=(1.02)^2*m

1.154=1.0404^m

take the log of both sides

ln(1.154)=m ln(1.0404)

m=ln(1.154)/ln(1.0404)

m=3.62 years

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