interest and discounts

Question

Calculate the simple interest :

A. $4,250 saved for 3months at annual rate of 3.5%? 

 

Calculate the amount for the following:

A. $158 saved for 2months at an annual rate of 4.5% compounded monthly?

Answer 1

For simple interest calculations, the rate for a period less than one year is simply the annual rate x (#of months/12).  For example, if we receive 10 percent interest for a period of 6 months, then we get 10% x 6/12 = 5%.  This makes sense because the period during which we are earning interest is 1/2 a year; therefore we get 1/2 the interest.

 

A. 4,250 x (3/12) x 0.035 = $37.19

 

The formula for annual compound interest is A = P (1 + r/n) ^ nt:
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for

 

Your question B is unclearly worded.  Do we want to learn the total amount returned to you or just the interest.  I'll assume it's the total amount.

 

Plug in your values to the formula  as follows:

 

A = 158 (1 + [0.045/12])^12*(2/12)     (Where 2/12 represents the portion of a year the money is invested for)

 

A = $159.19

 

Another way to think about this formula is that the rate you earn PER MONTH is .045/12 = 0.00375 and you earn it for a period of two months.