Question

A person invests 8000 dollars in a bank. The bank pays 7% interest compounded
annually. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 15600 dollars?
nt
A=P(1+
)
п

Answer 1

Answer:

The person must leave the money for around 9.9 years.

General Formulas and Concepts:
Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Algebra I

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtraction Property of Equality

Terms/Coefficients

Compounded Interest Rate Formula: $\displaystyle A = P \bigg( 1 + \frac{r}{n} \bigg)^{nt}$

• P is principle amount (initial amount)
• r is interest rate
• n is compounded rate
• t is time (in years)

Algebra II

Logarithms

• Logarithmic Property [Exponential]:                                                           $\displaystyle \log (a^b) = b \cdot \log (a)$

Step-by-step explanation:

Step 1: Define

Identify variables.

A = $15600

P = $8000

r = 0.07

n = 1

Step 2: Find Time Elapsed

1. Substitute in variables [Compounded Interest Rate Formula]:                 $\displaystyle 15600 = 8000 \bigg( 1 + \frac{0.07}{1} \bigg)^{1(t)}$
2. [Exponents] Simplify:                                                                                   $\displaystyle 15600 = 8000 \bigg( 1 + \frac{0.07}{1} \bigg)^{t}$
3. (Parenthesis) Simplify:                                                                                  $\displaystyle 15600 = 8000(1.07)^{t}$
4. [Division Property of Equality] Divide 8000 on both sides:                       $\displaystyle \frac{39}{20} = (1.07)^{t}$
5. [Equality Property] Log both sides:                                                             $\displaystyle \log \frac{39}{20} = \log (1.07)^{t}$
6. Simplify [Logarithm Property - Exponential]:                                              $\displaystyle \log \frac{39}{20} = t \log (1.07)$
7. [Division Property of Equality] Isolate t:                                                        $\displaystyle t = \frac{\log \frac{39}{20}}{\log 1.07}$
8. Evaluate:                                                                                                       $\displaystyle t = 9.87057$
9. Round:                                                                                                            $\displaystyle t \approx 9.9$

∴ it will take the person approximately 9.9 years investing $8,000 with a 7% interest rate compounded annually for them to obtain $15,600.

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Topic: Algebra II