Financial Math: Bank Loan versus Cash Advance

Question

Compare the cost of borrowing $4300 for six months (180 days) in the following two scenarios. How much will you save if you take out the bank loan as opposed to the cash advance?

1. You take out the money as a cash advance at 19.99%, compounded daily. Your creditor charges a cash advance fee of $5.
2. You take out a bank loan for the amount of the purchase at 6.75%, compounded monthly.

Answer 1

CalculateCash Advance Cost Formula: A=P(1+r/n}nt A=total future value P=Principal

P= 4,300 r=0.1999 n=365 days t= 6/12 months =0.5 years A=4,300(1+0.1999/365) 365x0.5

A=4,300(1.00054767)182. 5 = 4,751.87 Adding cash advance fee of 5 Total Cost = 4,751.87 + 5 =4,756.87 Cost of borrowing = 4,756.87- 4,300 = 4,756.87

Calculate Bank Loan Formula: Same A=total future value P=Principal

P = 4,300 r=6.75% = 0.0675 n=12 months t=0.5 years (6months) A=4,300(1+0.0675/12) 12x0.5

A=4,300(1+0.005625)6 A=4,447.18 Total Cost of Borrowing = 4,447-4,300 = 147

Compare: Net Savings(Loan vs.Advance): 309.69 4,756.87- 4,447.18 = 309.69

Choosing a Bank Loan rather than a credit card will reduce the borrowing cost by 309.69