$596.6 is the interest will you earn if you deposit $4000 into an account compounded semi-annually at 2.8% for 5 years.
What is compounding?
Compounding is the process whereby interest is credited to an existing principal amount as well as to interest already paid. Compounding thus can be construed as interest on interest—the effect of which is to magnify returns to interest over time, the so-called “miracle of compounding.”
According to question,$4000 into an account compounded semi-annually at 2.8% for 5 years.
We have to find interest rate.
Formula for compound interest is [tex]P[(1+i)^n-1][/tex]
Since compounding is semi-annually,
[tex]i=\frac{0.028}{2}[/tex][tex]=0.014[/tex] (since compounding is semi-annually)
[tex]n[/tex]=number of years=[tex]5[/tex] ×[tex]2=10[/tex] years (since compounding is semi-annually)
So, compound interest
[tex]=[/tex][tex]P[(1+i)^n-1][/tex]
[tex]=4000((1+0.014)^{10} -1))[/tex]
[tex]=4000[/tex]×[tex]0.1491[/tex]
[tex]=596.6[/tex]
Hence we can conclude that,$596.6 is the interest will you earn if you deposit $4000 into an account compounded semi-annually at 2.8% for 5 years.
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