Chapter 8.1, Problem 36E

To determine

To find:

Interest and the balance of the account for an account that earns simple annual interest.

Answer to Problem 36E

Interest: $1575

Balance of the account: $5775.

Explanation of Solution

Given:

Account details: $P=\$4200,r=5\%,t=7.5\text{ years}$

Concept used:

Simple interest formula - $I=P\cdot r\cdot t$ , where,

I = Amount of interest,

P = Principal amount,

r = Annual interest rate in decimal form,

t = Time in years.

Calculation:

Let us convert our given interest rate in decimal form as shown below:

  $5\%=\frac{5}{100}=0.05$

Upon substituting our given values in simple interest formula, we will get:

  $\begin{array}{l}I=P\cdot r\cdot t\left(\text{Simple interest formula}\right)\\ I=\$4200\cdot 0.05\cdot 7.5\left(\text{Substituting given values}\right)\\ I=\$1575\end{array}$

Therefore, the amount of interest would be $1575.

We know that final amount is account is principal amount plus amount of interest.

  $\begin{array}{l}\text{Final amount}=\text{Principal}+\text{Amount of interest}\\ \text{Final amount}=\$4200+\$1575\\ \text{Final amount}=\$5775\end{array}$

Therefore, the balance of the account would be $5775.