uta invests an amount into a compound interest investment account that pays 6% a year. after six years, she…

uta invests an amount into a compound interest investment account that pays 6% a year. after six years, she withdraws her total balance of $500. using the formula $a = p(1 + r)^t$, how much money did uta initially invest?\n$180.00\n$320.00\n$352.48\n$471.70

uta invests an amount into a compound interest investment account that pays 6% a year. after six years, she withdraws her total balance of $500. using the formula $a = p(1 + r)^t$, how much money did uta initially invest?\n$180.00\n$320.00\n$352.48\n$471.70

Answer

Explanation:

Step1: Identify the values in the formula

We know that $A = 500$, $r=0.06$ (since 6% = 0.06), and $t = 6$. The compound - interest formula is $A = P(1 + r)^t$, and we need to solve for $P$.

Step2: Rearrange the formula for $P$

Dividing both sides of the formula $A = P(1 + r)^t$ by $(1 + r)^t$, we get $P=\frac{A}{(1 + r)^t}$.

Step3: Substitute the values into the rearranged formula

Substitute $A = 500$, $r = 0.06$, and $t = 6$ into $P=\frac{A}{(1 + r)^t}$. So $P=\frac{500}{(1 + 0.06)^6}$.

Step4: Calculate $(1 + 0.06)^6$

$(1 + 0.06)^6=1.06^6\approx1.418519$.

Step5: Calculate $P$

$P=\frac{500}{1.418519}\approx352.48$.

Answer:

$352.48$ (C. $352.48$)