an investment of $45,000 earns 6% annual interest and is compounded semiannually. if no funds are added or removed from this account, what is the future value of the investment after 3 years?

An asset's future value is its worth on a particular date in the future. Alternatively, the future value is the sum of money that an investment will be worth, assuming a specified rate of return, after a specific amount of time (interest rate).

For finding the future value of a particular investment we can use the formula given below,

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

FV is the future value of the investment which is to be found.

PV is the present value of an investment which is given by,

PV= $45000

i is the annual interest rate.

i= 6%

But it is given it is semi-annually compounded. So, the rate of interest is calculated as

i =[tex]\frac{0.06}{2}[/tex]

n is the number of years.

n= 3 years

We multiply this number of 3 years 2 times to find the number of compoundings per year.

Therefore, 3×2 = 6 years.

So, by putting the above values in the formula we will get the,

[tex]45000(1+\frac{0.06}{2} )^{6}[/tex]

=45000×[tex]1.03^{6}[/tex]

=53732.34

Therefore, after 3 years, the future amount will be 53732.34$

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