Question

Janie took out a loan for $4850 at a 13.8% APR, compounded monthly, to buy
a backyard swimming pool. If she will make monthly payments of $455.50 to
pay off the loan, how many total payments will she have to make?​

Answer 1

Answer:

The total payment Janie have to make is $5466 .

Step-by-step explanation:

Given as :

The loan principal = $4850

The rate of interest applied = 13.8% compounded monthly

Let The time period of loan = t years

The monthly payment she make = $455.50 each month

I.e She make payment for t years = $455.50 × n

where n is the number of terms

From Compound Interest

Amount = Principal × $(1+\dfrac{\textrm rate}{12\times 100})^{12\times time}$

Or,  $455.50 × n  = $4850 × $(1+\dfrac{\textrm 13.8}{12\times 100})^{12\times time}$

Or, $\dfrac{455.50}{4850}$ × n  = $(1.0115)^{12\times 1}$

Or, 0.0939 × n  = $(1.0115)^{12}$

Or, 0.0939 × n = 1.14707

∴ n = $\dfrac{1.14707}{0.0939}$

I.e n = 12.21 ≈ 12

So, The number of terms Janie she will pay = 12

So, The total payment she have to make = $455.50 × 12 = $5466

Hence The total payment Janie have to make is $5466 . Answer

Answer 2

Answer:

She will have to make 12 payments

Step-by-step explanation: