1)
The assumption is made that the interest rate (APR) is effective. In order to analyze how the monthly payment is determined by the APR we start with turning our APR in to monthly interest rate:
rM=1+i1M-1
Where r/M is the interest rate for each month. The compound period is determined by M and APR is determined by i= 0,1575). rM=1+0,1575112-1=0,0122631252 The monthly interest rate is later added into the formula of Annuity because we have been given the value A= 21,87 with the above APR.
A=PrM1+rMN1+rMN-1≠21,87
P=1000 HKD in this case. N refers to the amount of interest periods, in this case 60. This equation should give us our present equivalent P. However it doesn’t which means there is something that’s’ missing. The handling fee will, according to the bank, be deducted from the final drawdown amount. In this case with P = (1000 HKD X 0.015 X 5 = 75 HKD). 1,5 % for 5 years (60 months).
→Include the handling fee and we will get the right result.
→A=1000-1000×0,015×60120,01226312521+0,0122631252601+0,012263125260-1=21,87
This shows how the monthly payment is determined by the APR.
Customers can use the monthly flat rate to calculate how much they will have to pay back or they can also use the APR and multiply by months. (withdraw the 1000)
1000+1000×0,052×60=1312
21,87×60=1312,2
The outcome in this case will be the same.
2)
In case 2 I use the same approach to se how the handling fee is included. I turn the APR (=19,77%) into monthly compound with rM=1+i1M-1 →1+19,77112-1=0,0151471604 and change the A=294,67 HKD, P=10 000 HKD and N = 48 periods. →A=PrM1+rMN1+rMN-1 →A=10 000×0,01514716041+0,0151471604481+0,015147160448-1=294,67
This time the value for A is coherent with the table presented by the bank for 48 months and tells us how the monthly payment is connected to the APR. If we
