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asked May 4, 2023 72.3k views

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Oskarth · Answer 1 · 2023-05-10T19:05:05+0000

Step-by-step explanation

Albert) Let's define

$\begin{cases}A=\text{ money earned from 1000 dollars and 1.2\% of annual interest compounded monthly,} \\ L=\text{ 2\% of 500 dollars, lost over the course of the ten years,} \\ B=\text{ money earned from 500 dollars growing compounded continuously at a rate of 0.8\% annually.}\end{cases}$

Then,

$M(\text{Albert})=A+(500-L)+B.$

To calculate A, we have the following compound interest formula:

$A=1000\cdot(1+(0.012)/(12))^(12\cdot10)\approx1127.43$

L is easy to calculate:

$L=0.02\cdot500=10.$

To calculate B, we have a formula as well:

$B=500\cdot e^(0.008\cdot10)\approx541.64.$

Then,

$M(\text{Albert})\approx1127.43+(500-10)+541.64=2159.07.$

Answer

The balance of Albert's $2000 after ten years is $2159.07.

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