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How do you determine the principal amount if you know that the interest is 4% and the...

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madison391 | eNotes Newbie

Posted August 23, 2013 at 6:45 PM via web

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How do you determine the principal amount if you know that the interest is 4% and the total payments being made equal $3,000,000 over 10 years. 

I need to determine what the original principal amount of the loan would equal.

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mariloucortez | High School Teacher | (Level 3) Adjunct Educator

Posted August 23, 2013 at 9:12 PM (Answer #2)

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Since nothing was said about what the exact kind of problem is this (say, simple interest, annuity or compound interest), based on the tags you provided, I assume that it is a compound interest problem.

By enumerating the given, it shows that it falls under compound interest problem.

So enumerating the given:
F = total payments/future value
P = principal value
i = interest in decimal per year
n = duration in years

It is also considered that the interest is annual since it is not specified. Rememeber to convert first the percentage to decimal before inputting it in your calculator. To do so, move the decimal point two times to the left. You can rewrite 4% as 4.0%.

F = $3,000,000
i = 4% = 0.04
n = 10 years
P = unknown

Given that, you can use the formula:

`P = F(1+i)^(-n)`

Substituting the given

`P = 3000000(1+0.04)^(-10)`

`P = $2026692.506`

Therefore, principal amount is $2026692.506.

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