Business Math

Question

I figured you would add the number of days left in the year from december to the number of the day for February 28 but that's not correct. Diane Van Os decided to buy a new car since her credit union was offering such low interest rates. She borrowed $30,500 at 4.75% on December 29 2012, and paid it off February 28 2014. How much did she pay in interest? (Assume ordinary interest.) (Use Days in a year table.) (Do not round intermediate calculations. Round your answer to the nearest cent.)

Answer 1

By ordinary interest I am going to assume you mean

interest that is compounded monthly.

 

The compound interest formula is   A = P(1+r/n)^nt

Where A = final amount paid

P = principal loan = $30,500

r = interest rate as decimal = .0475

n = number of times compounded per year = 12

t = time in years

 

For t I am assuming we count Dec 29th and Feb 28 so we have:

Dec 29, 30, 31 from 2012... all of 2013 ... and 31+28 = 59 days in 2014.

So, 1 full year plus 62 days = 1 62/365 years = 427/365 years for t

 

A = 30,500(1 + .0475/12)^12(427/365)

 

A = $32,239.28 as final amount paid

 

The interest is the difference between initial loan and final amount paid:

I = 32,239.28 - 30,500 = $1,739.28