Chapter 7.7, Problem 36PFA

To determine

To calculate:The balance of Robert’s account after 3 years.

Answer to Problem 36PFA

B. $28,611.75

Explanation of Solution

Given information:Robert invested $25,000 in an account that pays 4.5% interest compounded weekly.

Formula used:

Compound interest formula for compounded weekly is given by,

  $A=P{(1+\frac{\raisebox{1ex}{$R$}\!\left/ \!\raisebox{-1ex}{$52$}\right.}{100})}^{52t}$

where, $A=$ Amount

  $P=$ Principal

  $R=$ Rate % per annum

  $t=$ time

Calculation:

Here, $P=$ $25,000, $R=4.5\%$ , $t=3$ years.

Then, amount after 3 years is given by,

  $A=P{(1+\frac{\raisebox{1ex}{$R$}\!\left/ \!\raisebox{-1ex}{$52$}\right.}{100})}^{52t}$

  $\Rightarrow A=25000{(1+\frac{\raisebox{1ex}{$4.5$}\!\left/ \!\raisebox{-1ex}{$52$}\right.}{100})}^{52\cdot 3}$

  $\Rightarrow A=25000{(1+\frac{4.5}{5200})}^{156}$

  $\begin{array}{l}$ \Rightarrow A=25000{(1+.000865384615)}^{156}$$ \Rightarrow A=25000{(1.000865384615)}^{156}$\Rightarrow A=25000\times 1.14446779\\ \Rightarrow A=28611.7493\end{array}$

Rounding to nearest hundredths, $A=28611.75$

Thus, the balance of Robert’s account after 3 years will be $28611.75