Question

Marta deposits $15,000$ in an account with $7\%$ interest, compounded annually. How much will Marta’s account balance be after 15 years?

Answer 1

Hint:Since it is clearly given that the interest is compounded annually, Try to understand what does compound interest mean and note down it’s definition first. After this step state the formula for calculating the compound interest and substitute all the values given to us and calculate.

Complete step by step answer:
First we will try to understand what is compound interest.Compound interest is defined as the process where the interest increases exponentially rather than linearly. This simply means that instead of accepting the interest on a particular investment you reinvest the original money invested along with the interest. This process continues and the returns start to grow overtime.Compound interest is calculated by certain formula which is given as follows,
$A = P{\left( {1 + r} \right)^n}$
Where, A= final amount, P=Initial amount, r=interest and n=no of years.
In our given case,
$P=15,000\\
\Rightarrow r=7\%\\
\Rightarrow r= \dfrac{7}{{100}} \\
\Rightarrow r= 0.07$
$n$=15years
substituting all this values in our formula we get
$A = P{\left( {1 + r} \right)^n} \\
\Rightarrow A= 15000{\left( {1 + 0.07} \right)^{15}} \\
\Rightarrow A= 15000 \times 2.759031 \\
\therefore A= 41385.465 \\ $
Hence Marta will have $41385.47 after 15years.

Note:It is not necessary to write briefly about compound interest. You just have to state what is compound interest and start with the correct formula directly. No logic is required in this kind of straight forward questions where you just have to use the formula and conclude with your answer.