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Interest and maturity value

Leslie Hart borrowed $15,900 to pay for her child’s education at Riverside Community College. Leslie must repay the loan at the end of 6 months in one payment with 3 3\4% interest.

a)

How much interest must Leslie pay?(Do not round intermediate calculation. Round your answer to 2 decimal places. Omit the "$" sign in your response.)

Interest $?

b)

What is the maturity value?(Do not round intermediate calculation. Round your answer to 2 decimal places. Omit the "$" sign in your response.)

Maturity value $

Comments

Lets define some variables. 

PV = Present Value = $15,900

FV = Future Value or Maturity Value is unknow

i = annual interest rate (written as a decimal)

t = time in years that interest will accrue

Interest $ = FV - PV

In general using simple interest, FV = PV( 1 + i*t) = PV + PV*i*t; and using compound interest, FV = PV(1+i)^t. 

NOTE that when t=1, simple and compound will result in the same answer.

Assuming the 3 3/4% = 3.75% = .0375 is the rate that will be charged for the 6 months, the time and period match (like when t=1 above) and using simple and compound interest will result in the same.  Here t=1 which is a full 6 months:

FV = 15900 (1.0375) =16496.25 and Interest $ = 15900(.0375)*1 = 596.25

Assuming simple interest and 3.75% is an annual rate, [6 months = .5 year or 1 year/2] FV = 15900 (1 + .0375/2) = 16198.13 and Interest $ = 298.13 .

Assuming compound interest at 3.75% is an annual rate, FV = 15900 (1+.0375)^.5 = 16195.38 and Interest $ = 295.38.

Simple interest is usually used for periods less than 1 year (since they result in higher amounts for the lender).  I do believe that the problem is assuming that the 3.75% is for the 6 month period since interest is asked for first and simple or compound interest interest was not specified.

So Leslie Hart must pay 596.25 in interest and the maturity value is 16496.25.

 

i had the same answers also, but my homework online said it was wrong.. just checking did you round to the 2 decimal places.... sometimes I get mess up with rounding.. thank you for your help....

My question is why is Leslie Hart paying $15.900 for a community college in the first place.   I really hate to see numbers like this.  A good college consultant should have steered Leslie Hart in a better direction.

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1 Answer

To find the interest we simply do this: 15,900 × 0.0375 × 6/12

So are interest should be: $298.13

For the maturity value we can use a formula: MV = P + I

So lets plug in the numbers to the formula and we get: 15,900 + 298.13

So we simply add them now and we can say the maturity value is $16,198.13

Please check this with your business teacher because I'm not sure 100% sure of this.