Question

A deposit of $2000 is invested in an account earning 4.5% interest compounded monthly. How much money will there be in 6 years? Equation:Answer:

Answer 1

Step-by-step explanation:

Given;

We are told that a deposit of $2000 is invested in an account that yields an annual interest of 4.5%, but is compounded monthly.

Required;

We are required to calculate how much money will be in the investment in 6 years time.

Step-by-step solution.

The formula for calculating a compound interest is given as;

`A=P(1+r)^t`

The variables in this formula are;

`\begin{gathered} A=amount\text{ }after\text{ }the\text{ }period\text{ }given \\ P=principal\text{ }amount\text{ }at\text{ }the\text{ }beginning \\ r=annual\text{ }rate\text{ }of\text{ }interest \\ t=period\text{ }of\text{ }investment\text{ }in\text{ }years \end{gathered}`

However, when the compounding is done at several periods within a year (for example, monthly, quarterly, half-yearly, etc), the formula is amended to reflect the period of compounding within each year.

The amended formula is what we have been given in this question.

Therefore, from the details provided,

`\begin{gathered} P=2000 \\ r=0.045 \\ t=6 \\ n=12 \end{gathered}`

Please note that n is the number of times compounding takes place per year and in this case its 12 times (monthly).

Therefore;

`A=2000(1+(0.045)/(12))^(12*6)`
`\begin{gathered} A=2000(1+0.00375)^(72) \\ \\ A=2000(1.00375)^(72) \\ \\ A=2000*1.30930310151 \\ \\ A=2618.60620301 \end{gathered}`

Rounded to the nearest hundredth, we now have

ANSWER:

`A=2,618.61`