Answer:
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
* <em>The total number of the payments is 18</em>