Question

A depositor opens a new savings with $4000 at 8% compounded semiannual. At the beginning of year 5, an additional $5000 is deposited. At the end of six years. what is the balance in the Account? The balance in the account at the end of 6 years is $

Answer 1

In order to find the value of the investment, we can use the following equation:

`P=P_0(1+(r)/(n))^(nt)`

Where P is the final value, P0 is the initial value, r is the annual rate, t is the amount of time and n is a factor that depends on the compound interval (for a semiannual compound, we have n = 2).

So for the first period of 4 years, we have that:

`\begin{gathered} P=4000(1+(0.08)/(2))^(2\cdot4) \\ P=4000(1+0.04)^8 \\ P=4000(1.04)^8 \\ P=4000\cdot1.368569=5474.28 \end{gathered}`

Then, we had an addition of 5000, so the new initial value is:

`5474.28+5000=10474.28`

Now, for the next 2 years, we have that:

`\begin{gathered} P=10474.28(1+(0.08)/(2))^(2\cdot2) \\ P=10474.28(1.04)^4 \\ P=10474.28\cdot1.169859=12253.43 \end{gathered}`

So the final value at the end of 6 years is $12,253.43