Question

Carl deposited P dollars into a savingsaccount that earned 8 percent annual interest,compounded semiannually. Carl made noadditional deposits to or withdrawals from theaccount. After one year, the account had a totalvalue of $10,816. What was the value of P ?

Answer 1

The amount deposited is

`=P`

The number of times compounded is semi-annually, that is

`n=2`

The time t is

`t=1`

The rate at which P was compounded semi-annually is

`r=8\%=0.08`

The amount in the account after one year is

`A=10,816`

Concept:

The formula for compound interest is given below as

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

By substituting the values, we will have

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ 10,816=P(1+(0.08)/(2))^(2*1) \\ 10,816=P(1+(0.08)/(2))^2 \\ \end{gathered}`

By solving for the value of P, we will have

`\begin{gathered} 10,816=P(1+(0.08)/(2))^2 \\ 10,816=P(1+0.04^{})^2 \\ 10,816=P(1.04)^2 \\ 10,816=P*1.0816 \\ \text{divide both sides by 1.0816} \\ (10,816)/(1.0816)=(P*1.0816)/(1.0816) \\ P=10,000 \end{gathered}`

Hence,

The value of P = 10,000