Question

Problem 3 • A student is hard up for rent money and decides to explore a quick cash loan company. The company offers to loan the student $500 today to cover rent at an interest rate of 1% per day, with the balance due (principal and interest) in one month. How much will the student owe the company at the end of the month (assume a month with 30 days)? • If the company offers instead to have him make 12 equal monthly payments over the course of a year at a 0.5% daily rate, how much will he have to pay each month to pay off the $500? How much will he have paid in interest?

Answer 1

For the first case of payment in one month time:

Future value of loan = Principle*(1+daily interest rate)^30

Future value of loan = 500*(1+1%)^30

Future value of loan = $673.92

Student will owe the company an amount of $673.92 after the end of one month.

For the second case when the payment is done in 12 monthly installments.

Daily interest rate = .5%

Monthly interest rate = (1+.5%)^30 -1 = 16.14%

Time = 12 months

Let, monthly payment = P

Then,

500 = P*(1-1/1.1614^12)/.1614

P = 500/5.167

P = $96.77                                                                               

So, monthly payment will be $96.77 to pay off the loan.

Monthly component of the interest payment is illustrated in following amortization schedule.

			Loan Amount =	500
			Monthly Interest =	16.14%
Month	monthly instalment	Interest paid	Principal paid	Loan amount left for the payment
1	96.77	80.7	16.07	483.93
2	96.77	78.11	18.66	465.27
3	96.77	75.09	21.68	443.59
4	96.77	71.60	25.17	418.42
5	96.77	67.53	29.24	389.18
6	96.77	62.81	33.96	355.22
7	96.77	57.33	39.44	315.78
8	96.77	50.97	45.80	269.98
9	96.77	43.58	53.19	216.79
10	96.77	34.99	61.78	155.01
11	96.77	25.02	71.75	83.25
12	96.77	13.44	83.33	-0.08

Total interest paid = $661.16