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Logan and Rita each open a savingsaccount with a deposit of $8,100. Logan'saccount pays 5% simple interest annually.Rita's account pays 5% interestcompounded annually. If Logan and Ritamake no deposits or withdrawals over thenext 4 years, what will be the difference intheir account balances?$125.60$104.05$113.22$134.89

Sagot :

Answer:

[tex]\text{ \$125.60}[/tex]

Explanation:

Here, we want to get the difference in the account balance of two people. One who deposits with a simple interest return and another with a compound interest return

For Logan:

[tex]\begin{gathered} Amount\text{ = Interest\lparen I\rparen + Principal\lparen P\rparen} \\ I\text{ = }\frac{PRT}{100} \\ \\ A\text{ = }\frac{PRT}{100}\text{ + P} \\ \\ A\text{ = P\lparen}\frac{RT}{100}+\text{ 1\rparen} \end{gathered}[/tex]

Where P is the amount deposited which is $8,100

R is the rate which is 5%

T is the time which is 4 years

Substituting the values:

[tex]\begin{gathered} A\text{ = 8100\lparen}\frac{5\times4}{100}\text{ + 1\rparen} \\ \\ A\text{ = 8100\lparen0.2+1\rparen} \\ A\text{ = 8100\lparen1.2\rparen} \\ A\text{ = \$9,720} \end{gathered}[/tex]

For Rita:

Here, we want to get the amount for a compounding deposit type

[tex]A\text{ = P\lparen1 + }\frac{r}{n})\placeholder{⬚}^{nt}[/tex]

where P is the principal which is $8,100

r is the rate which is 5% = 5/100 = 0.05

n is the number of times interest is compounded yearly which is 1 (since it is annual)

t is the number of years which is 4

Substituting the values, we have it that:

[tex]\begin{gathered} A\text{ = 8100\lparen1 + }\frac{0.05}{1})\placeholder{⬚}^{4\times1} \\ A\text{ = 8100\lparen1.05\rparen}^4\text{ = \$9,845.60} \\ \end{gathered}[/tex]

Finally, we proceed to get the difference

Mathematically, we have that as:

[tex]9845.60\text{ -9720 = \$125.60}[/tex]

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