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To save for a car when he turns 18, Pascale deposited $500 each year into a savings account with a 7.5% interest rate compounded annually. Using the formula, what is the value of the account at the end of the fifth year?



Answer :

Answer:

$717.81

Step-by-step explanation:

Compound Interest Formula (Yearly)

The formula that the problem refers to is,

                                        [tex]A=P(1+\dfrac{r}{n} )^n^t[/tex],

where A is the amount, P is the principal or initial amount, r is the rate in decimal form, n is the number of times the interest is compounded in a year and t is the time that elapses in years.

Applying the Formula

Reading the problem, all the variables of the formula can be found,

  • the $500 Pascale deposited is his principal amount or, P
  • 0.075 is the 7.5% interest rate in decimal form or, r
  • n = 1 as the problem states the interest being compounded annually or once a year
  • t = 5 as the problem asks for the value of the account in 5 years.

Plugging all those values into the formula, the final answer is,

[tex]A=500(1+\dfrac{0.075}{1} )^1^(^5^)[/tex]

[tex]=500(1.075)^5\\\\\Longrightarrow A= 717.81[/tex].

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