Daily · 2026-05-04

Three problems · Compound Interest, Logarithms, Quadratic Equations

One bite-sized math problem set for the day. Read the statement, think it through, then expand the solution to check your reasoning.

#1 · Compound Interest·Easy

You deposit \$1,000 in an account paying 5% annual interest, compounded yearly. How much is in the account after 3 years?

A.\$1,150.00
B.\$1,157.63
C.\$1,500.00
D.\$1,050.00

Solution

Compound interest:

A = P(1 + r)^t = 1000 \cdot (1.05)^3 = 1000 \cdot 1.157625 = \

1{,}157.63

.Note how each year's interest is calculated on the previous year's balance, not the original principal — that's why compounding beats simple interest by ~\

7.63 over three years here.

The everyday version of

A = P(1+r)^t

. Most people instinctively compute

P + Prt

(simple interest, \

1,150) and stop. The \

7.63 gap is the entire idea of compounding — small in three years, devastating in thirty.

#2 · Logarithms·Easy

What is the value of

\log_2 32 - \log_2 4

A. $3$
B. $8$
C. $28$
D. $\log_2 28$

Solution

Using the quotient rule:

\log_2 32 - \log_2 4 = \log_2 \dfrac{32}{4} = \log_2 8 = 3

(since

2^3 = 8

).

Alternatively, evaluate each term:

\log_2 32 = 5

\log_2 4 = 2

, so

5 - 2 = 3

Two routes to the same answer. The quotient rule is mechanical; evaluating each term is concrete. Doing it both ways is how the rule stops being a black box.

#3 · Quadratic Equations·Medium

Find the sum of the roots of

x^2 - 7x + 12 = 0

A. $3$
B. $4$
C. $7$
D. $12$

Solution

By Vieta's formulas, for

x^2 + bx + c = 0

the sum of the roots is

-b

. Here

b = -7

, so the sum is

7

.

Verification by factoring:

x^2 - 7x + 12 = (x - 3)(x - 4)

, so the roots are

3

and

4

, summing to

7

Vieta's formulas turn root-questions into coefficient-arithmetic — no need to actually solve the equation. For a contest setting, this is the difference between 10 seconds and 60 seconds.

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