A man borrows 8550 A payment of 304 is made 61 days later A

A man borrows $8550. A payment of $304 is made 61 days later. A second payment of $1590 is paid 132 days after the first payment. A third payment of X is due 46 days after the second payment, after which the loan balance is 0. The loan is charged a simple interest rate of r = 3.25%. What is X, if the Declining Balance Method is used?

Solution

The man borrowed = $8550

He paid = $ 304

time period = 61 days = 61/365 years

interest rate = 3.25% = .0325

Interest = 8550* 61/365*.0325

= $ 46.439

the amount to principal which is the payment made minus the interest due = 304 - 46.439 = $ 257.561

the principal remaining = 8550 - 257.561 = $ 8292.439

now the interest on the remaining principal = 8292.439*132/365*.0325

                                                                    = $ 97.464

the amount to principal which is the payment made minus the interest due = 1590 - 97.464 = 1492.536

the principal remaining = 8292.439 - 1492.536 = $ 6799.903

now the interest on the remaining principal = 6799.903*46/365*.0325 = $ 27.852

the amount to principal which is the payment made minus the interest due = X - 27.852

the principal remaining = 0

6799.903 - (X - 27.852) = 0

=> X = $ 6827.755