Multiple choice

Catherine puts $\$ 1,100$ in an investment account that she expects will make $5\%$ interest for each three month period. However, after a year she realises she was wrong about the interest rate and she has $\$ 50$ less than she expected. Assuming the interest rate the account earns is constant, which of the following equations expresses the total amount of money, $x$, she will have after $t$ years using the actual rate?

  1. $x=1,100(1.04)^{4t}$
  2. $x=1,100(1.05)^{4t-50}$
  3. $x=1,100(1.04)^{t/3}$
  4. $x=1,100(1.035)^{4t}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The expected amount was 1100(1.05)^(4t). The actual amount is 50 less, but the question asks for the equation using the actual rate. Since the interest is compounded every 3 months (4 times a year), the rate per period is 4% (1.04) to result in the observed difference.

AI explanation

Catherine expected to earn 5% interest each three-month period, which means she expected to have $1100 * (1.05)^4 after one year. This calculation gives an expected total of $1334.46, but she actually has \$50 less, making her actual amount \$1284.46. The actual annual multiplier is therefore 1284.46 / 1100 = 1.16769, and taking the fourth root gives a quarterly multiplier of approximately 1.03963. Using the standard compound interest formula, the total amount of money x after t years is x = 1100(1.04)^{4t}.

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