Question

Mr. Diego deposits $2,000 into an account with four and one half percent ( 4 1/2) interest compounded twice per year. How much will be in the account in 2 years?

Answer 1

$2186.17

Step-by-step explanation:

The amount in the account after 2 years can be calculated using the following equation:

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

Where P is the initial amount, r is the interest rate, n is the number of times the interest is compound per year and t is the number of years.

The interest rate is 4 1/2 % which is equivalent to 4.5% or 0.045 because:

`4(1)/(2)=4+(1)/(2)=4+0.5=4.5`

Then, replacing P by $2,000, r by 0.045, n by 2, and t by 2 years, we get:

`\begin{gathered} A=2000(1+(0.045)/(2))^(2\cdot2) \\ A=2000(1+(0.045)/(2))^4 \\ A=2000(1+0.0225)^4 \\ A=2000(1.0225)^4 \\ A=2000(1.093) \\ A=2186.17 \end{gathered}`

Therefore, after 2 years there will be $2186.17 in the account.