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nikitadnepr [17]
3 years ago
12

1.

Mathematics
1 answer:
olchik [2.2K]3 years ago
8 0
To solve this we are going to use the future value of annuity ordinary formula: FV=P[ \frac{(1+ \frac{r}{n} )^{kt} -1}{ \frac{r}{n} } ]
where
FV is the future value
P is the periodic payment
r is the interest rate in decimal form
n is the number of times the interest is compounded per year
k is the number of payments per year
t is the number of years

We know for our problem that P=6200 and t=5. To convert the interest rate to decimal form, we are going to divide the rate by 100%:
r= \frac{6}{100} =0.06
Since the deposit is made semiannually, it is made 2 times per year, so k=2.
Since the type of the annuity is ordinary, payments are made at the end of each period, and we know that we have 2 periods, so n=2.
Lets replace the values in our formula:

FV=P[ \frac{(1+ \frac{r}{n} )^{kt} -1}{ \frac{r}{n} } ]
FV=6200[ \frac{(1+ \frac{0.06}{2} )^{(2)(5)} -1}{ \frac{0.06}{2} } ]
FV=71076.06

We can conclude that the correct answer is <span>$71,076.06</span>
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\text{The scientific notation:}\\\\a\times10^n\\\\1\leq a


a.\\(5\times10^3)\times(3.5\times10^{-1})=(5\times3.5)\times(10^3\times10^{-1})\\\\=15.75\times10^{3+(-1)}=15.75\times10^2=1.575\times10\times10^2\\\\=1.575\times10^{1+2}=\boxed{1.575\times10^3}

b.\\(8\times10^2)\div(4\times10^3)=(8\div4)\times(10^2\div10^3)=2\times10^{2-3}\\\\=\boxed{2\times10^{-1}}

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