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A student loan can be taken either at 8% for 15 years or 6% for 20 years. The student...

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steve1234 | Student, Undergraduate | Salutatorian

Posted September 23, 2013 at 2:26 PM via web

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A student loan can be taken either at 8% for 15 years or 6% for 20 years. The student is not allowed to close the loan earlier. If the stident needs $25000 what is the total amount payable in both the cases.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 23, 2013 at 2:35 PM (Answer #1)

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The students needs a student loan of $25000. Assume that the entire amount can be paid back at the end of the loan tenure.

If the first option of making an interest payment of 8% for 15 years is chosen, the total amount due after 15 years is `25000*(1 +0.08)^15` = 79304.22

One the other hand, if the student takes the loan at an interest rate of 6% for 20 years, the amount payable after 20 years is `25000*(1+0.06)^20 ` = 80178.38

The total amount payable by the student is $79304.22 if the loan is taken for 15 years at an interest rate of 8%; if it is taken for 20 years at an interest rate of 6%, the amount due is $ 80178.38

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steveschoen | College Teacher | (Level 3) Assistant Educator

Posted September 23, 2013 at 2:38 PM (Answer #2)

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Hi, steve,

In each case, we can follow a formula:

F = P*(1+r)^t

F = final value

P = Present or principal value

t = time in years.

For this, we are given the principal value, $25,000.  We are given each rate as well as each time.  So, plugging in the numbers:

For 8% at 15 years

F = 25000*(1+0.08)^15 = $79,304.23

For 6% at 20 years

F = 25000*(1+0.06)^20 = $80,178.39

Good luck, Steve.  I hope this helps.

Till Then,

Steve

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