Question

For an account that earns simple annual interest, find the interest and the balance of the account.

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

Short answer

Interest: $1575

Balance of the account: $5775

Step-by-step solution

Step 1. Given Information.

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

Step 2. Concept Used.

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

I = Amount of interest,

P = Principal amount,

r= Annual interest rate in decimal form,

t = Time in years.

Step 3. Calculation.

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

$\begin{array}{c}5\%=\frac{5}{100}\\ =0.05\end{array}$

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

$\begin{array}{l}I=P\cdot r\cdot t\left(\text{Simpleinterestformula}\right)\\ I=\$4200\cdot 0.05\cdot 7.5\left(\text{Substitutinggivenvalues}\right)\\ I=\$1575\end{array}$

Therefore, the amount of interest would be $1575.

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

$\begin{array}{l}\text{Finalamount}=\text{Principal}+\text{Amountofinterest}\\ \text{Finalamount}=\$4200+\$1575\\ \text{Finalamount}=\$5775\end{array}$

Step 4. Conclusion.

The balance of the account would be $5775.