 stop2dance3l

2021-12-27

Clare made $160 babysitting last summer. She put the money in a savings account that pays 3% interest per year. If Clare doesnt ### Answer & Explanation SlabydouluS62 Skilled2021-12-28Added 52 answers Step 1 Given Initial amount:$160
$rate=3\mathrm{%}$ interest per year
Step 2
Final amount after n years is given by
$A={A}_{0}{\left(1.03\right)}^{n}$
Where
$A=$ final amount
${A}_{0}=$ initial amount
$n=$ no of years
$A=160{\left(1.03\right)}^{n}$ (1)
Step 3
a) After 5 years
Put $n=5$ in the expression (1)
$A=160{\left(1.03\right)}^{n}$
$A=160{\left(1.03\right)}^{5}$
$A=160\left(1.1592740743\right)$
$A=185.483851$
$A\approx 185.48$
Step 4
b) Expression for the amount of money Clare would have after 30 years is
$A=160{\left(1.03\right)}^{30}$ psor32

Solution
Clare made $160 babysitting last summer. She put the money in a saving account that pays 3% interest per year. It is a condition of compound interest with annually compounding. We know that, ${P}^{\prime }=P{\left(1+r\right)}^{n}$ Where, ${P}^{\prime }=$ the money she will be getting after n years, $P=\text{the money she deposited}=\mathrm{}160$ $r=\text{annual rate of interest}=3\mathrm{%}=0.03$ $n=\text{number of years}$ $⇒{P}^{\prime }=160{\left(1+0.03\right)}^{1}=160×1.03=\mathrm{}164.8$ This is why when she multiply 1.03 with her current amount, she gets the amount she will be getting after one year. Money she will be getting after 2 year Taking current balance as$164.8 as at the end of one year it will be the base amount on which interest will be calculated,
$⇒{P}^{\prime }=168.8{\left(1+0.03\right)}^{1}=168.8×1.03=\mathrm{}169.74$
Again by multiplying 1.03 she can get the amount of money she will be getting next year.
Money she will be getting after 5 year
${P}^{\prime }=\text{the money she will be getting after 5 years}$,
$P=\text{the money she deposited}=\mathrm{}160$
$r=\text{annual rate of interest}=3\mathrm{%}=0.03$
$n=5$
Putting the values,
$⇒{P}^{\prime }=160{\left(1+0.03\right)}^{5}=160×1.1593=\mathrm{}185.49$
She will be getting $185.49 after 5 years. We can also do this by calculating the amount of money she will be getting at the end of each year and multiplying it with 1.03 in order to get the amount of money she will be getting the next year. Expression for the amount of money Clare would have after 30 years if she never withdraws money from the account $⇒{P}^{\prime }=160{\left(1+0.03\right)}^{3}0$ This is the expression for the desired condition. karton Expert2022-01-04Added 613 answers Answer: Given, amount(A)=$160 ate(r)=3% Since it is given that by multiplying current ammount by 1.03 we can get amount she will have next year means that After one year Amount =160 * 1.03 =$164.80 (current amount after one year) After two years Amount P=164.80 * 1.03 =$169.74 Therefore, amount after 2 years is \$169.74

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