Question

Sana had two equal outstanding loans, one from 135 days ago and one from 81 days ago. She repays both loans today with the single amount of $14800. If interest is 7% on the loans, what was the size of the equal amounts borrowed?

Answer 1

Let each loans amount borrowed be X.

For simple interest, accumulated value of loan is:

Total accumulated amount = Principal + (Principal x rate x time)

Accumulated value for 1^st loan = X + X x 0.07 x 135/365

                                                        = X + X x 0.07 x 0.36986301369863

                                                        = X + 0.0258904109589041 X

                                                        = X (1+ 0.0258904109589041)

                                                        = 1.0258904109589041 X

Accumulated value for 2^nd loan = X + X x 0.07 x 81/365

                                                        = X + X x 0.07 x 0.221917808219178

                                                        = X + 0.015534246575343 X

                                                        = X (1+ 0.015534246575343)

                                                        = 1.015534246575343 X

Total amount to pay = 1.0258904109589041 X + 1.015534246575343 X

           $ 14,800 = X (1.0258904109589041 + 1.015534246575343)

                           = 2.0414246575342466 X

X = $ 14,800/2.0414246575342466

   = $ 7,249.83895211509 or $ 7,250

Size of equal amounts borrowed is $ 7,250