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

She will have to make 12 payments

Explanation:

Answer 2

The total payment Janie have to make is $5466 .

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+(\textrm rate)/(12* 100))^(12* time)`

Or, $455.50 × n = $4850 ×
`(1+(\textrm 13.8)/(12* 100))^(12* time)`

Or,
`(455.50)/(4850)` × n =
`(1.0115)^(12* 1)`

Or, 0.0939 × n =
`(1.0115)^(12)`

Or, 0.0939 × n = 1.14707

∴ n =
`(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