Mitchell took out a loan for $1100 at a 19.2% apr, compounded monthly, to
buy a scanner. if he will make monthly payments of $71.50 to pay off the
loan, how many total payments will he have to make?
оа. 18
ов. 19
ооо

The total number of the payments is 18 ⇒ answer A

Step-by-step explanation:

* Lets revise the rule of compounded monthly payment

→ , where

- A is the loan amount

- r is monthly interest in decimal (R/12*100))

- n the total number of payments

∵ A = $1100

∵ EMI = $71.5

- Interest rate is 19.2% APR

∵ r =

- Substitute these values in the rule to find n

∴ 71.5 =

- By using cross multiplication

∴ 71.5[1 - ] = 17.6

- Divide both sides by 71.5

∴ 1 - =

- Subtract 1 from both sides

∴ - = -

- Multiply both sides by -1

∴ =

- By using cross multiplication

∴ 49[ ] = 65

- Divide both sides by 49

∴ =

- Insert log for both sides

∴ ㏒ = log( )

- Put n in-front of the ㏒

∴ n㏒(1.016) = ㏒( )

- Divide both sides by ㏒(1.016)

∴ n = 17.8 ≅ 18

* The total number of the payments is 18

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step-by-step explanation:

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