Question

You borrow $325 for 30 days at a simple interest rate of 2.5%.What is the interest on the loan? Be sure to use the Bankers' Rule when working with daily rates.What is the loan's future value?

Answer 1

Simple interest formula:

`I=P\cdot r\cdot t`

I is the interest

P is the principal amount

r is the interest rate in decimals

t is the time in years

Future value formula (A):

`A=P(1+r\cdot t)`

___________

For the given situation:

1. Turn the time into years:

Bankers' Rule: 1 year is 360days

`30\text{days}\cdot\frac{1\text{year}}{360\text{days}}=(1)/(12)\text{years}`

2. Write the interest rate in decimal form:

`(2.5)/(100)=0.025`

What is the interest on the loan?:

`\begin{gathered} I=325\cdot0.025\cdot(1)/(12) \\ \\ I=0.68 \end{gathered}`

The interest of the loan is $0.68

What is the loan's future value?

You can use the formula above or just add he interest to the principal amount:

`\begin{gathered} A=325(1+0.025\cdot(1)/(12)) \\ \\ A=325.68 \end{gathered}`

The loan's future value is $325.68