Question

Austin invested $11,000 in an account paying an interest rate of 5.7% compoundedquarterly. Assuming no deposits or withdrawals are made, how much money, to thenearest dollar, would be in the account after 6 years?

Answer 1

The amount in the account after six years is $15,448

Here, we want to calculate the amount that would result from compounding a deposit

To calculate this, we shall be using the compound interest formula

That would be;

`\begin{gathered} A\text{ = P(1 + }(r)/(n))^(nt) \\ \\ \text{where A is the amount made from the compounding} \\ P\text{ is the money deposited = \$11,000} \\ r\text{ is the interest rate which is 5.7\% = }(5.7)/(100)\text{ = 0.057} \\ n\text{ is the number of times per year the interest is componded} \\ \sin ce\text{ it is quarterly, n= 4} \\ t\text{ is the number of years = 6 years} \end{gathered}`

Substituting all these values into the equation, we have that;

`\begin{gathered} A\text{ = 11,000(1 + }(0.057)/(4))^(4*6) \\ \\ A=11,000(1+0.01425)^(24) \\ \\ A=11,000(1.01425)^(24) \\ \\ A\text{ = 15,448} \end{gathered}`