Question

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The simple interest on a savings account is directly proportional to the amount of the investment. A savings account with $4000 earns $90.00 after 1 year. Find a mathematical model that gives the interest N after 1 year in terms of the amount invested P.

Answer 1

N = 0.0225P

Explanation:

`\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I = Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}`

Given:

• P = $4000
• I = $90
• t = 1 year

Substitute the given values into the simple interest formula and solve for r to find the interest rate:

`\implies 90=4000 \cdot r \cdot 1`

`\implies 90=4000r`

`\implies r=(90)/(4000)`

`\implies r=0.0225`

Therefore, the simple interest rate is 2.25%.

Given:

• N = interest
• P = principal
• r = 2.25% = 0.0225
• t = 1 year

Substitute the given values into the formula to create a mathematical model that gives the interest N after 1 year in terms of the amount invested P:

`\implies N=P \cdot 0.0225 \cdot 1`

`\implies N=0.0225P`