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I have this practice question from my ACT prep guide, THE SUBJECT IS PRE CALC!! MEANING ITS HARD AND COMPLEX. Below will be the questions to this problem ( includes 5 questions )1. What is the balance of Albert’s $2000 after 10 years? 2. What is the balance of Marie’s $2000 after 10 years? 3. What is the balance of Han’s $2000 after 10 years?4. What is the balance of Max’s $2000 after 10 years? And lastly, 5. Who is $10,000 richer at the end of the competition?

I have this practice question from my ACT prep guide, THE SUBJECT IS PRE CALC!! MEANING-example-1
User Cgp
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Albert

Compound interest formula:


A=P(1+(r)/(n))^(nt)

where:

A: final amount

P: principal

r: annual interest rate, as a decimal

t: time in years

n: number of times interest applied per year

Substituting with P = $1000, r = 0.012 (= 1.2/100), n = 12 (interest is compounded monthly), t = 10 years, we get:


\begin{gathered} A=1000(1+(0.012)/(12))^(12\cdot10) \\ A=1000(1.001)^(120) \\ A=1127.43\text{ \$} \end{gathered}

If $500 lost 2%, then it keeps 98% of its original value, that is,

$500x98% = $490

Continuous compound formula:


A=Pe^(rt)

where the variables have the same meaning as before.

Substituting with P = $500, r = 0.008 ( = 0.8/100), and t = 10 years, we get:


\begin{gathered} A=500\cdot e^(0.008\cdot10) \\ A=541.64\text{ \$} \end{gathered}

The balance of Albert’s $2000 after 10 years is:

$1127.43 + $490 + $541.64 = $2159.07

Marie

Substituting in the compound interest formula with P = $1500, r = 0.014 (= 1.4/100), n = 4 (interest is compounded quartely), t = 10 years, we get:

User Chemoish
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