Answer to Question #238243 in Financial Math for anu188

Question

Village Finance Co. advanced three loans to Kamiko—$4,200 on June 20, $3,800 on August 25,and $3,300 on October 29. Simple interest at 8.25% was charged on all three loans, and all were repaid on December 31 when some bonds that she owned matured. What total amount was required to pay off the loans?

Answer 1

Loan 1 = 4200$ taken on June 20

Loan 2 = 3800$ taken on August 25

Loan 3 = 3300$ taken on October 29

Loans will be repaid on 31st December

So the interest will be charged till 30th December

For loan 1 , the tenure of loan will be = June (11 days) including the 20th of June + July (31 days ) + aug (31days) + sep (30days) + Oct(31days) + Nov(30days) + dec(30days)

= 194 days

So time =t= 194/365

Interest charged =r= 8.25% annually , that is for 365 days

Interest charged on loan for its tenure = P×r×t /100 =

(4200×8.25×194)/(365×100) = 184.17

Amount required to close loan1 = 4200+184.17 = 4384.17 $

Similarly for loan2 = number of days = 7(aug) + 30(sep) + 31 (Oct) + 30 (Nov) + 30 (dec) = 128 days

Time = 128/365

Interest =( 3800×8.25×128)/(100×365) = 109.94$

Amount required to close loan2 = 3800+108.94= 3908.94

Similarly for loan3 tenure of loan = 3(Oct) + 30 (Nov) + 30 (dec) = 63 days

So interest charged = (3300×8.25×63)/(100×365) = 46.99

So amount required to close loan3 = 3300+46.99 = 3346.99

Total amount required to payoff the loans = 4384.17+ 3908.94 + 3346.99 = 11640.1 $