Question

diana had $2272 in her account after 6 years. if the account paid 7% (or 0.07) interest, how much did diana initially deposit in the account? m = p(1 + rt)
what was dianas initial deposit?
$\square$ (simplify your answer.)

Explanation:

Step1: Identify given values

We know that \( M = 2272 \), \( R = 0.07 \), \( T = 6 \), and the formula is \( M = P(1 + RT) \). We need to solve for \( P \).

Step2: Rearrange the formula to solve for \( P \)

Starting with \( M = P(1 + RT) \), we can divide both sides by \( (1 + RT) \) to get \( P=\frac{M}{1 + RT} \).

Step3: Calculate \( 1 + RT \)

First, calculate \( RT \): \( RT=0.07\times6 = 0.42 \). Then, \( 1 + RT=1 + 0.42=1.42 \).

Step4: Solve for \( P \)

Substitute \( M = 2272 \) and \( 1 + RT = 1.42 \) into the formula for \( P \): \( P=\frac{2272}{1.42} \). Calculating this division, \( \frac{2272}{1.42}=1600 \).

Answer:

\( 1600 \)