Question

Mary deposited $4000 into an account with 2.1% interest, compounded semiannually. Assuming that no withdrawals are made, how much will she have inthe account after 5 years?Do not round any intermediate computations, and round your answer to the nearest cent.

Answer 1

First, divide the annual interest by 2 to find the semmiannual rate:

$\frac{(2.1\text{ \%})}{2}=1.05\text{ \%}$

Each six months period, the current amount of money in the account gets a 1.05% increase. There are 10 periods of 6 months in a time interval of 5 years. Then, the 1.05% increase is appliead 10 times over the $4000 initial deposit.

To apply an increase of 1.05% is the same as multiplying the initial amount by a factor of:

$\begin{gathered} 1+\frac{1.05}{100}=1+0.0105 \\ =1.0105 \end{gathered}$

To apply that increase 10 times is the same as multiplying the initial amount by a factor of 1.0105 10 times, which is the same as multiplying the initial amount by a factor of:

$(1.0105)^{10}$

Then, the amount of money that she will have in the account after 5 years, is:

$4000\times(1.0105)^{10}=4440.411$

Therefore, the amount of money in the account after 5 years to the nearest cent, is:

$4440.41$