Question

Help with algebra 2 question

Answer 1

Given that Dani has 2000 in a investment account that earns 3% per year compound monthly.

Part A).

The compound interest formula:

Compound interest can be calculated using the formula

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

where,

A(t) is the account value,

t is measured in years,

P is the starting amount of the account, often called the principal, or more generally present value,

r is the annual percentage rate (APR) expressed as a decimal, and

n is the number of compounding periods in one year.

Now, Part B).

initial amount = 2000

annual percentage rate = 3%

Compounding period = 12

So,

`A(t)=(1+(r)/(n))^(nt)`

Further,

`\begin{gathered} 3500=2000(1+(0.03)/(12))^(12t) \\ (3500)/(2000)=(1+(0.03)/(12))^(12t) \\ \ln 1.75=12t\ln 1.0025 \\ t=(1)/(12)(\ln 1.75)/(\ln 1.0025) \\ t=18.67 \end{gathered}`

Hence, t = 18.67 is the answer for part B.