Chapter 7.7, Problem 8CYU

To determine

To calculate:The worth of Paul’s investment in 8 years.

Answer to Problem 8CYU

The worth of Paul’s investment in 8 years is $620.46

Explanation of Solution

Given information:Paul invested $400 into an account with a 5.5% interest rate compounded monthly.

Formula used:

Compound interest formula for compounded monthly is given by,

  $A=P{(1+\frac{\raisebox{1ex}{$R$}\!\left/ \!\raisebox{-1ex}{$12$}\right.}{100})}^{12t}$

where, $A=$ Amount

  $P=$ Principal

  $R=$ Rate % per annum

  $t=$ time

Calculation:

Here, $P=$ $400, $R=5.5\%$ , $t=8$ years.

Then, amount after 8 years is given by,

  $A=P{(1+\frac{\raisebox{1ex}{$R$}\!\left/ \!\raisebox{-1ex}{$12$}\right.}{100})}^{12t}$

  $\Rightarrow A=400{(1+\frac{\raisebox{1ex}{$5.5$}\!\left/ \!\raisebox{-1ex}{$12$}\right.}{100})}^{12\cdot 8}$

  $\Rightarrow A=400{(1+\frac{0.458333}{100})}^{96}$

  $\begin{array}{l}$ \Rightarrow A=400{(1+.00458333)}^{96}$$ \Rightarrow A=400\times {(1.00458333)}^{96}$\Rightarrow A=400\times 1.55114663\\ \Rightarrow A=620.458652\end{array}$

Rounding to nearest hundredths, $A=620.46$

Thus, the worth of Paul’s investment in 8 years is $620.46