# Your total payment on a 4 year loan, which charged 10.1 % simple interest, amounted to $ 46200. How much did you originally borrow?

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The total amount paid is $46,200; the interest rate is 10.1%; the time is 4 years. We are asked to find the original loan amount.

The original loan amount we will designate as P (for principal). The interest rate, R, is 10.1% or .101. The length of the loan is 4 years. We are told that we are charged simple interest -- we assume the interest rate is a yearly rate and the interest is applied yearly.

Then the total amount paid is the principle plus the intereste. The interest is calculated as I=PRT where P is the principal, R is the interest rate per period, and T is the number of periods. (Usually the rate is an annual rate, and T is the number of years.)

Thus 46200=P+PRT

46200=P(1+RT) Now substitute R=.101 and T=4 to get:

46200=P(1.404)

`P~~32905.98 `

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The original loan amount was $32905.98

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There are possible complications: we assumed no payments. (Some loans are structured this way; no payments or reduced payments are made for some period of time when the balance becomes due. This is called a balloon payment.)

Given: time t=4, interest rate 10.1% r=.101 , total loan payment A= $46,200.

Find out how much was originally borrowed, P.

Use the formula `A=P(1+r)^t`

Substitute in the given information. Then solve for P.

`46200=P(1+.101)^4`

`46200=P(1.101)^4`

`46200/1.101^4=P`

`31440.74=P`

The amount originally borrowed is $31,440.74.

Let us the value originally we borrowed is P.

Annual interest rate = 10.1%

So the interest for 4 years =` Pxx10.1/100xx4`

Total amount paid `= P+Pxx10.1/100xx4 = 46200`

`P(1+10.1xx4/100) = 46200`

`P = 32905.89 `

**So the original amount borrowed is $32906 (as an approximation)**