Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?
A. w/(1+1.08)
B. w/(1.08+1.16)
C. w/(1.16+1.24)
D. w/(1.08+1.08^2)
E. w/(1.08^2+1.08^2)
OA D
Source: Official Guide
Alex deposited x dollars into a new account that earned 8
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\(1.08(1.08x + x) = (1.08^2)x + 1.08x\)
The new total value obtained is equal to \(w\), we can set up the following equation:
\(w = (1.08^2)x + 1.08x\)
So, \(X\) in terms of \(w\)
\(w = x(1.08^2 + 1.08)\)
\(w/(1.08^2 + 1.08) = x\)
Therefore, __D__ is the correct option.
The new total value obtained is equal to \(w\), we can set up the following equation:
\(w = (1.08^2)x + 1.08x\)
So, \(X\) in terms of \(w\)
\(w = x(1.08^2 + 1.08)\)
\(w/(1.08^2 + 1.08) = x\)
Therefore, __D__ is the correct option.
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We start by determining the new value of the x dollars Alex deposited into his account that earned 8 percent annual interest. At the end of the first year the amount of money in the account was 1.08x and then he added another x dollars to the account, so the account then had a total value of 1.08x + x dollars. The 1.08x + x dollars earned another 8 percent interest for the year. Thus, the total value of his account at the end of the second year is:BTGmoderatorDC wrote:Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?
A. w/(1+1.08)
B. w/(1.08+1.16)
C. w/(1.16+1.24)
D. w/(1.08+1.08^2)
E. w/(1.08^2+1.08^2)
OA D
Source: Official Guide
1.08(1.08x + x) = (1.08^2)x + 1.08x
Since the new total value is equal to w, we can set up the following equation:
w = (1.08^2)x + 1.08x
Now we must get x in terms of w.
w = x(1.08^2 + 1.08)
w/(1.08^2 + 1.08) = x
Answer: D
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