Question

You deposit $3000 in an account that
earns simple interet at an annual rate of
5%. How long must you leave the money
in the account to earn $500 in interest?

Answer 1

Answer:

3 ¹/₃ years

Step-by-step explanation:

Simple Interest Formula

I = Prt

where:

• I = Total interest.
• P = Principal amount.
• r = Annual interest rate (in decimal form).
• t = Time (in years).

Given:

• I  = $500
• P = $3,000
• r = 5% = 0.05

Substitute the given values into the formula and solve for t:

$\sf \implies 500=3000 \times 0.05 \times t$

$\sf \implies 500=150t$

$\sf \implies t=\dfrac{500}{150}$

$\implies \sf t=3\frac{1}{3}$

Therefore, the money must be left in the account for 3 ¹/₃ years for the account to earn $500 interest.

Answer 2

GiveN:-

• Principal = $3,000
• Rate = 5% = 0.05
• Interest = $500 years

To FinD:-

• Interest = ??

SolutioN:-

$\\ \diamond{\underline{\underline{\sf {\color{red}{\;Calculating \; Time \; :-}}}}}$

$\\ \qquad{\underline{\boxed {\bf{ Interest (I)= \: P \times R \times T}}} }\red\bigstar$

$\\ \sf \implies \: Interest (I)= \: P \times R \times T$

$\\ \sf \implies \: 500= \: 3000 \times 0.05 \times t$

$\\ \sf \implies \: 500= \: 3000 \times 0.05t$

$\\ \sf \implies \: 500= \: 150t$

$\\ \sf \implies \: 150t= \: 500$

$\\ \sf \implies \: t= \: \frac{500}{150}$

$\\ \sf \implies \: t= \: \frac{50\cancel{0}}{15\cancel{0}}$

$\\ \sf \implies \: t= \: \cancel{\frac{50}{15}}$

$\\ \sf \implies \: t= \ 3.5$

$\\{\implies{\red {\underline {\boxed{ \sf { Time= \ 3.5 \: years}}}}}}\purple\bigstar$

$\\ \qquad{ \underline{\rule{120pt}{2pt}}}$