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The apr of deloris' savings account is 3.8%, and interest is compounded semiannually. if the principal in deloris' savings account were $13,700 for an entire year, what would be the balance of her account after all the interest is paid for the year?

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nobillionaireNobley
The future value of the balance in a savings account, PV, with an apr of r% compounded t times a year for n years is given by:

[tex]FV=PV\left(1+ \frac{r}{t} \right)^{nt}[/tex]

Given that the apr of deloris' savings account is 3.8%, and interest is compounded semiannually. if the principal in deloris' savings account were $13,700 for an entire year, the balance of her account after all the interest is paid for the year is given by

[tex]FV=13,700\left(1+ \frac{0.038}{12} \right)^{12\times1} \\ \\ 13,700(1+ 0.0032)^{12}=13,700(1.0032)^{12} \\ \\ 13,700(1.0387)=\bold{\$14,229.76}[/tex]
spicetothemax

Answer:

Deloris' account balance would be $14,225.55 after one year.

Explanation:

The formula [tex]FV=PV(1+\frac{r}{n})^{nt}[/tex] is used to find compound interest.

FV = result or final amount

PV = starting or principal amount

r = annual interest rate (as a fraction)

n = number of compounds a year (semiannually is 2, quarterly is 4...)

t = number of years

Now we can plug and solve:

[tex]FV=13,700(1+\frac{0.038}{2})^{2(1)}[/tex] = [tex]13,700(1+0.019)^2[/tex] = [tex]13,700(1.019)^2[/tex] = [tex]13,700(1.038361)[/tex]

= $14,225.55

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