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question 5 practice similar questions
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a college student has invested 5000 in an account that pays 2.9% interest compounded weekly. which of the following equations could be used to find the amount in the account after 8 years?
a (5000)(0.029)(8)
b ( 5000 e^{0.029 \times 8} )
c ( 5000left(1+\frac{2.9}{52}
ight)^{52 \times 8} )
d ( 5000left(1+\frac{0.029}{52}
ight)^{52 \times 8} )
e ( 5000 e^{2.9 \times 8} )
f none of the above
submit answer attempts: 0/4
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Explanation:

Step1: Recall the compound - interest formula

The compound - interest formula is \(A = P(1+\frac{r}{n})^{nt}\), where \(P\) is the principal amount (\(P = 5000\)), \(r\) is the annual interest rate (as a decimal, \(r=0.029\)), \(n\) is the number of times interest is compounded per year (\(n = 52\) for weekly compounding), and \(t\) is the number of years (\(t = 8\)).

Step2: Substitute the values into the formula

Substitute \(P = 5000\), \(r = 0.029\), \(n = 52\), and \(t = 8\) into the formula \(A=P(1 +\frac{r}{n})^{nt}\). We get \(A = 5000(1+\frac{0.029}{52})^{52\times8}\).

Answer:

D. \(5000(1+\frac{0.029}{52})^{52\times8}\)