Question

find the value of the investments at the end of 5 years for the following compounding methods , semiannual, monthly, daily

Answer 1

Given:

There are given that the total amount is 34900 dollars

Step-by-step explanation:

According to the question:

We need to find the value of the investment.

So,

To find the value of investments, we need to use the compound interest formula:

So,

From the formula of compound interest:

(a): For annually:

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

Then,

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ A=34900(1+(0.08)/(1))^5 \end{gathered}`

Then,

`\begin{gathered} A=34,900(1+(0.08)/(1))^(5) \\ A=34900(1+0.08)^5 \end{gathered}`

Then,

`\begin{gathered} A=34,900(1+0.08)^(5) \\ A=34900(1.08)^5 \\ A=34900(1.46) \\ A=51279.55 \end{gathered}`

Now,

(b): For the semiannual:

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ A=P(1+(r)/(2))^(2t) \end{gathered}`

Then,

`\begin{gathered} A=P(1+(r)/(2))^(2t) \\ A=34900(1+(0.08)/(2))^(2(5)) \end{gathered}`

Then,

`\begin{gathered} A=34900(1+(0.08)/(2))^(2(5)) \\ A=34900(1+0.04)^(10) \end{gathered}`

Then,

`\begin{gathered} A=34900(1+0.04)^(10) \\ A=34900(1.04)^(10) \\ A=34900(1.48) \\ A=51660.5 \end{gathered}`

(c): For monthly:

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ A=P(1+(r)/(12))^(12t) \end{gathered}`

Then,

`\begin{gathered} A=P(1+(r)/(12))^(12t) \\ A=P(1+(r)/(12))^(12(5)) \\ A=P(1+(0.08)/(12))^(12(5)) \end{gathered}`

Then,

`\begin{gathered} A=34900(1+(0.08)/(12))^(12(5)) \\ A=34900(1+0.0067)^(60) \\ A=34,900(1.0067)^(60) \end{gathered}`

Then,

`\begin{gathered} A=34900(1.0067)^(60) \\ A=34900(1.49) \\ A=52099.02 \end{gathered}`

And,

(d): For daily:

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ A=P(1+(r)/(365))^(365(5)) \end{gathered}`

Then,

`\begin{gathered} A=P(1+(r)/(365))^(365(5)) \\ A=34900(1+(0.08)/(365))^(365(5)) \\ A=34,900(1+0.000219)^(365(5)) \end{gathered}`

Then,

`\begin{gathered} A=34,900(1+0.000219)^(365(5)) \\ A=34,900(1.000219)^(1825) \\ A=34,900(1.49) \\ A=52140.53 \end{gathered}`

Final answer:

Hence, the all values is shown below:

`\begin{gathered} (a).Annual:51279.55 \\ (b).Semiannual:51660.5 \\ (c).Monthly:52099.02 \\ (d).Daily:52140.53 \end{gathered}`