Calculates the Principal that produced an interest of $650 at the rate of 4 % per annum in 150 days? Calculate using simple interest rate assumption?

The first thing I'll do is figure out what the actual percentage is that we're working with. We're told that the rate is 4% per annum - that is the percentage increase we'd be working with if the money was invested for an entire year. But it wasn't. It was invested for 150 days. Which means our percentage is:

With that, we can now look at the interest and principal amounts.

Think of the calculation this way: If I had $100 in principal and it made 1.7$1.70 in interest. And so looking at this question a different way, I could say that if I divided the amount of interest by the percentage, I'd get the principal:

We can do the same with our numbers:

To calculate the principal that produced an interest of $650 at the rate of 4% per annum in 150 days using the simple interest rate assumption, you can use the formula for simple interest:

[ I = P \times R \times T ]

Where:

• ( I ) is the interest earned,
• ( P ) is the principal amount (the initial amount of money),
• ( R ) is the annual interest rate (in decimal form),
• ( T ) is the time the money is invested or borrowed for (in years).

Since the interest rate is given as 4% per annum, or 0.04 in decimal form, we need to calculate the time ( T ) in years.

Given that there are 365 days in a year, we divide 150 days by 365 to get ( T ):

[ T = \frac{150}{365} ]

[ T ≈ 0.41096 \text{ years} ]

Now, we can rearrange the formula to solve for the principal ( P ):

[ P = \frac{I}{R \times T} ]

Substituting the given values:

[ P = \frac{650}{0.04 \times 0.41096} ]

[ P ≈ \frac{650}{0.01644} ]

[ P ≈ 39530.7239 ]

Therefore, the principal that produced an interest of $650 at the rate of 4$39,530.72.