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Jessica opened a bank account that earns 2 percent interest compounded annually. Her initial deposit was $100, and she uses the expression $100(x)t to find the value of the account after t years. Jessica’s friend Tyshaun found an account that earns2.5 percent interest compounded annually. Tyshaunmade an initial deposit of $100 into this account atthe same time Jessica made a deposit of $100 into heraccount. After 10 years, how much more money willTyshaun’s initial deposit have earned than Jessica’sinitial deposit? (Round your answer to the nearestcent and ignore the dollar sign when gridding yourresponse.)



Answer :

Money earned by Tyshaun’s initial deposit when compared to  Jessica’s initial deposit is 6.11.

What is the Compound Interest formula ?

The compound interest equation be

[tex]$A=P(1+r/100)^{t}[/tex]

Given: Jessica's account, P = $100, t = t, r = 2%

Tyshaun's account, P = $100, t = t, r = 2.5%

Amount expression = $ [tex]100(x)^{t}[/tex]

The compound interest equation be

[tex]$A=P(1+r/100)^{t}[/tex]

substitute the values in the above equation, we get

[tex]$= 100(1 + 2/100)^t[/tex]

simplifying the above equation, we get

[tex]$=100(1+0.02)^{t}[/tex]

[tex]$=100(1.02)^{t}[/tex]

On comparing with the given expression, [tex]100(x)^{t}[/tex]

x = 1.02(Jessica's account)

Therefore, the value of x = 1.025 (Tyshaun's account)

The money earned by Tyshaun’s initial deposit when compared to Jessica’s initial deposit after 10 years:

Tyshaun's  earning = [tex]100(1.025)^{10}[/tex] = $128.01

Jessica's earning= [tex]100(1.02)^{10}[/tex]= $121.9

Tyshaun's  earning-Jessica's earning = $128.01 - $128.01 = 6.11

Therefore, money earned by Tyshaun’s initial deposit when compared to  Jessica’s initial deposit is 6.11.

To learn more about compound interest, refer to:

https://brainly.com/question/24924853

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