Jackie K.

asked • 10/19/12# 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 $

## 1 Expert Answer

Michael H. answered • 10/20/12

Your kid having trouble in school?

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.

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Terri M.

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.

NOTEthat 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.

10/19/12