Daily Math Problems — May 4, 2026: Compound Interest, Logarithms, Quadratic Equations

Problems & worked solutions

International

Problem 1 — Compound Interest

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

Show answer & worked solution

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

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.

International

Problem 2 — Logarithms

What is the value of $\log_{2} 32 - \log_{2} 4$ ?

Show answer & worked solution

A. $3$ ✓ correct
B. $8$
C. $28$
D. $\log_{2} 28$

Using the quotient rule: $\log_{2} 32 - \log_{2} 4 = \log_{2} \frac{32}{4} = \log_{2} 8 = 3$ (since $2^{3} = 8$ ).

Alternatively, evaluate each term: $\log_{2} 32 = 5$ , $\log_{2} 4 = 2$ , so $5 - 2 = 3$ .

International

Problem 3 — Quadratic Equations

Find the sum of the roots of $x^{2} - 7 x + 12 = 0$ .

Show answer & worked solution

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

By Vieta's formulas, for $x^{2} + b x + c = 0$ the sum of the roots is $- b$ . Here $b = - 7$ , so the sum is $7$ .

Verification by factoring: $x^{2} - 7 x + 12 = (x - 3) (x - 4)$ , so the roots are $3$ and $4$ , summing to $7$ .

Problems & worked solutions

International

Problem 1 — Compound Interest

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

Show answer & worked solution

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

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.

International

Problem 2 — Logarithms

What is the value of $\log_{2} 32 - \log_{2} 4$ ?

Show answer & worked solution

A. $3$ ✓ correct
B. $8$
C. $28$
D. $\log_{2} 28$

Using the quotient rule: $\log_{2} 32 - \log_{2} 4 = \log_{2} \frac{32}{4} = \log_{2} 8 = 3$ (since $2^{3} = 8$ ).

Alternatively, evaluate each term: $\log_{2} 32 = 5$ , $\log_{2} 4 = 2$ , so $5 - 2 = 3$ .

International

Problem 3 — Quadratic Equations

Find the sum of the roots of $x^{2} - 7 x + 12 = 0$ .

Show answer & worked solution

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

By Vieta's formulas, for $x^{2} + b x + c = 0$ the sum of the roots is $- b$ . Here $b = - 7$ , so the sum is $7$ .

Verification by factoring: $x^{2} - 7 x + 12 = (x - 3) (x - 4)$ , so the roots are $3$ and $4$ , summing to $7$ .