A real estate agent knows that he will receive a commission of $4,250 from the s
ID: 2564380 • Letter: A
Question
A real estate agent knows that he will receive a commission of $4,250 from the sale of a property when the deal is completed 37 days from now. Needing cash today, though, he signs a discount note at a credit union, using his expected commission as the maturity value. The discount rate is 9.55%. Find the effective rate (APR).
A plumbing contractor recieve proceeds of $4,1713.53 on a 12.5% simple discount note with a face value of $5,000. Find the time of the note in days.
You are due a $750 paycheck at the end of the week (Friday), but want to get your hands on the cash on Monday. A payday lender offers to make this deal with you for a fee of 2% of the paycheck. What is the rate you are paying for this service? Assume a 365-day year.
Explanation / Answer
.Discount rate=9.55%
37 days interest =9.55*(37/365)= 0.968082%=0.00968082
Effective rate of interest (APR)=R
(1+R)=(1+0.00968081)^(365/37)= 1.099704
R=0.099704
Effective rate of interest (APR)=9.9704%
Present value=P=$4,171.353
Future value=F=$5,000
F=P*(1+i)
i=interest
Annualized interest=12.5%=0.125
Assume number of days =n
Interest for n number of days=(n/365)*0.125
F=P*(1+(0.125*(n/365))
5000=4171.353*(1+(0.125*(n/365))
*(1+(0.125*(n/365))=5000/4171.353=1.198652
1+(0.125*(n/365)= 1.198652
0.125*(n/365)= 0.198652
n/365=0.198652/0.125=1.589216
n=365*1.589216=580.0638 days
Number of days=580.0638
$750 paycheck
Number of days=4
Amount of fees=2% of 750=$15
Rate paid for this service in 4 days=0.02
Rate paid in 365 days=0.02*(365/4)
Annual rate for this service=0.02*(365/4)= 1.825
Rate in percent=182.5%
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