Question

Sue Stitch buys a sewing machine. The price, including tax, is $575.00. She finances the sewing machine over 24 months after making a $25 down payment. The true annual interest rate is 15%. What are Sue's monthly payments (principal plus interest)?

To the nearest penny, c = $

Total of payments = amount financed + c = $

Total of payments ÷ number of payments = monthly payment = $

Answer 1

Hi there!

To the nearest penny, c = $85.94.

Total of payments = amount financed + c = $635.94.

Total of payments ÷ number of payments = monthly payment = $26.50

Your friend, ASIAX

Answer 2

c = $85.94

Total payment = $635.94

Total payment ÷ Number of payment = $26.5.

Explanation:

We are given that,

The tax on the machine = $575 with down payment = $25. Also, the rate of interest = 15% i.e. 0.15 and time period = 24 months.

Now, the principal amount = tax - down payment = $575 - $25 = $550.

Then, the monthly payment by the annuity formula is given by,

`c=(r * PV)/(1-(1+r)^(-n) )`

i.e.
`c=(0.15 * 550)/(1-(1+0.15)^(-24) )`

i.e.
`c=(82.5)/(1-(1.15)^(-24) )`

i.e.
`c=(82.5)/(1-0.035 )`

i.e.
`c=(82.5)/(0.965)`

i.e.
`c=85.94`

Hence, c = $85.94

Thus, total payment = amount financed + c = $550 + $85.94 = $635.94.

So, Total payment ÷ Number of payment =
`(635.94)/(24)` = $26.5.