Rhiannahas$83,350inasavingsaccountthatearns6%interestperyear.Theinterestisnotcompounded.Tothenearestcent,howmuchwillshehaveintotalin8months?

Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.

Round your answer to the nearest cent.

1 answer

To calculate the total amount Rhianna will have in her savings account after 8 months, we can use the formula for simple interest:

\[ i = prt \]

Where:

  • \( p \) is the principal amount (the initial amount of money),
  • \( r \) is the annual interest rate in decimal form,
  • \( t \) is the time in years,
  • \( i \) is the interest earned.

Given:

  • \( p = 83,350 \)
  • \( r = 6% = 0.06 \)
  • \( t = \frac{8}{12} = \frac{2}{3} \) years (since 8 months is two-thirds of a year)

First, we will calculate the interest \( i \):

\[ i = 83,350 \times 0.06 \times \frac{2}{3} \]

Calculating this step-by-step:

  1. Calculate \( 0.06 \times \frac{2}{3} \):

    \[ 0.06 \times \frac{2}{3} = 0.06 \times 0.6667 \approx 0.04 \]

  2. Now calculate the interest \( i \):

    \[ i = 83,350 \times 0.04 = 3,334 \]

Now we will find the total amount in the account after 8 months by adding the interest earned to the principal:

\[ \text{Total Amount} = p + i = 83,350 + 3,334 = 86,684 \]

Thus, Rhianna will have a total of \( \text{$86,684.00} \) after 8 months.