Daily Math · 2026-05-07

Question 1

A credit card charges $24\%$ APR, compounded monthly. What's the effective annual rate (EAR)?

Accepted Answer

The monthly rate is $24\%/12 = 2\%$. Compounding 12 times: $(1.02)^{12} \approx 1.2682$, so EAR $\approx 26.82\%$.

The published 'APR' understates what you actually pay because it ignores compounding. EAR is the apples-to-apples comparison.

Answer

Exactly $24\%$

Answer

About $26.8\%$

Answer

About $28.5\%$

Answer

About $124\%$

Question 2

If $\log_2 x + \log_2 (x - 6) = 4$, what is $x$?

Accepted Answer

Combine: $\log_2 [x(x-6)] = 4$, so $x(x-6) = 2^4 = 16$, i.e. $x^2 - 6x - 16 = 0$.

Factor: $(x - 8)(x + 2) = 0$, giving $x = 8$ or $x = -2$.

**Check the domain.** $\log_2 x$ requires $x > 0$, and $\log_2(x-6)$ requires $x > 6$. Only $x = 8$ satisfies both, so $x = 8$ is the only valid solution.

Answer

$x = 2$

Answer

$x = 8$

Answer

$x = -2$

Answer

Both $8$ and $-2$

Question 3

How many ways can you arrange the letters of 'BANANA'?

Accepted Answer

Total letters: 6. Repeats: 3 A's, 2 N's, 1 B.

Distinct permutations $= \dfrac{6!}{3! \cdot 2! \cdot 1!} = \dfrac{720}{6 \cdot 2} = \dfrac{720}{12} = 60$.

The denominator divides out the orderings we'd otherwise double-count by treating the three A's as distinguishable.

Answer

$60$

Answer

$120$

Answer

$360$

Answer

$720$

Problems & worked solutions

Problem 1 — Compound Interest

Problem 2 — Logarithms

Problem 3 — Combinatorics