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Sagot :
Given:
Account 1:
Principal, P = $2000
Time, t = 4 years
Rate, r = 3% = 0.03
number of times compounded, n = monthly = 12 months/year
Account 2:
Principal, P = $2200
Time, t = 2 years
Rate, r = 5% = 0.05
number of times compounded, n = daily = 365 days/year
Let's determine the account which will earn more interest.
Apply the compound interest formula:
[tex]I=(P(1+\frac{r}{n})^{nt})-P[/tex]Where:
P is the Principal
r is the interest rate
n is the number of times the ineterest is compounded per unit time'
t is the time in years
Now, let's find the interest earned in each account.
• ACCOUNT 1:
[tex]\begin{gathered} I=(2000(1+\frac{0.03}{12})^{12\times4})-2000 \\ \\ I=(2000(1+0.0025)^{48})-2000 \\ \\ I=(2000(1.0025)^{48})-2000 \\ \\ I=2254.66-2000 \\ \\ I=254.66 \end{gathered}[/tex]
The interest earned in account 1 is $254.66
• ACCOUNT 2:
[tex]\begin{gathered} I=(2200(1+\frac{0.05}{365})^{730})-2200 \\ \\ I=(2200(1+0.00013698)^{730})-2200 \\ \\ I=2431.36-2200 \\ \\ I=231.36 \end{gathered}[/tex]
The interest earned in account 2 is $231.36
We can see the interest earned in account 1 is greater than the interest earned in account 2.
To find the difference, we have:
$254.66 - $231.36 = $23.30
Therefore, Account 1 earns $23.30 more than Account 2.
ANSWER:
Account 1 earns $23.30 more than Account 2.
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