Question

Lonnie needs extra money to buy a truck to start up a delivery service. He takes out a simple 16) interest loan for $4000.00 for 3 months at a rate of 5.25% . How much interest must he pay, and what is the future value of the loan?

Answer 1

The interest Lonnie must pay is $52.50, and the future value of the loan is $4,052.50.

Step-by-step explanation:

To calculate the interest, we can use the formula:

Interest = Principal * Rate * Time

Substituting the given values:

Interest = 4000 * 0.0525 * (3/12) = $52.50

The future value of the loan can be calculated using the formula:

Future Value = Principal + Interest

Substituting the values:

Future Value = 4000 + 52.50 = $4,052.50

Answer 2

well, since a year has 12 months, 3 months are just 1/4 of a year, so let's use that.

`~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$4000\\ r=rate\to 5.25\%\to (5.25)/(100)\dotfill &0.0525\\ t=years\to (3)/(12)\dotfill &(1)/(4) \end{cases} \\\\\\ A=4000[1+(0.0525)((1)/(4))]\implies A=4000\left( (1621)/(1600) \right)\implies \boxed{A=4052.5} \\\\\\ \stackrel{interest~paid}{4052.5~~ - ~~4000\implies \boxed{52.5}}`