Question

Vince borrows $900 to buy a couch. He will pay off the loan by paying 1.5% simple interest for 2 years. Vince incorrectly calculates the amount he will pay back using the expression below. 900 + 900(1.015 • 2) What is the correct amount Vince will pay back altogether? Explain the error in Vince’s expression.

Answer 1

`\bf ~~~~~~ \textit{Simple Interest Earned Amount}\\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to& \$900\\ r=rate\to 1.5\%\to (1.5)/(100)\to &0.015\\ t=years\to &2 \end{cases} \\\\\\ A=900(1+0.015\cdot 2)\implies A=\stackrel{\stackrel{recall}{\mathbb{PEMDAS}}}{900(1+0.03)}\implies A=900(1.03)`

Answer 2

Answer : The correct expression of amount Vince will pay back altogether is,
`\$ 900+((\$900)* (1.5)* (2))/(100)`

Step-by-step explanation :

Given:

Principle = $900

Rate = 1.5 %

Time = 2 years

First we have to determine the simple interest.

Formula used :

`S.I=(PRT)/(100)`

where,

P = principle

R = interest rate

T = time

S.I = simple interest

Now put all the given values in the above formula, we get the expression for simple interest.

`S.I=((\$900)* (1.5)* (2))/(100)`

Now we have to determine the amount he will pay back.

Amount = Principle + Simple interest

Amount =
`\$ 900+((\$900)* (1.5)* (2))/(100)`

This is the correct expression of amount Vince will pay back altogether.

The given expression is wrong because in this expression divide by 100 not done.

Thus, the correct expression of amount Vince will pay back altogether is,
`\$ 900+((\$900)* (1.5)* (2))/(100)`