Respuesta :
Joni is mistaken because she applied the compounding rate formula rather than just the simple interest rate equation, which is incorrect. $231.53 will belong to her.
Explain the term compounded annually?
- The equation A=P(1+r)t can be used to calculate the amount A you would have after t years if you deposit P dollars together in savings account including an annual interest rate of r and also the interest is compounded annually.
The $200 was deposited by Joni into an account that earned interest at a 5% annual compound rate.
Joni calculated and she'll have a final balance of $230 after three years.
The steps are as following,
- P = 200, r = 5, t = 3
- I = 200*0.05* 3
- I = 30
- 30 + 200 = 230
Because Joni employed the simple interest rate method instead of the compound interest rates formula, she is mistaken $231.53 will belong to her.
The yearly compound interest rate if 5% is stated above.
As a result, she ought to have used the compound interest calculation when calculating.
A = P(1 + r/n)∧(nt)
Amount then becomes:
A = 200(1 + 0.05)³
A = $231.53.
Thus, final amount will be obtained as $231.53.
To know more about the compounded annually, here
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The complete question is-
Joni put $200 in an interest-bearing account with an annual compound interest rate of 5%. Joni determined that after 3 years, she will have a total balance of $230. Her work is shown below. Step 1: P = 200, r = 5, t = 3 Step 2: I = 200 ∙ 0.05 ∙ 3 Step 3: I = 30 Step 4: 30 + 200 = 230 Is Joni correct? Explain. Joni is not correct, because $230 is just the interest she will earn; she will have $430 total. Joni is not correct; $230 will be her balance after 1 year. After 3 years, she will have $290. Joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. She will have $231.53. Joni is correct. She correctly applied the I = P · r · t formula, and will have $230.
