Question

Victoria invested her savings in an account at 4% p.a. simple interest for 10 months. Ifshe earned an interest amount of $225 at the end of the term, what was the principalamount of the investment?

Answer 1

Simple interest formula:

`\begin{gathered} A=P(1+r\cdot t) \\ \\ A=\text{Amount} \\ P=\text{Principal} \\ r=\text{Interest rate (in decimal form)} \\ t=\text{time (in years)} \end{gathered}`

To find the Principal amount solve P:

`P=(A)/(1+r\cdot t)`

1. Turn the time into years:

`10\text{months}\cdot\frac{1\text{year}}{12\text{months}}=(5)/(6)\text{year}`

2. Turn the interest rate into decimals:

`(4)/(100)=0.04`

3. Substitute the values and evaluate the formula to find P:

`P=(225)/(1+0.04\cdot(5)/(6))\approx217.74`

Then, the principal investment required to get a total amount of $225 at a rate of 4% in 10 months is $217.74