Question 2
Ho is now saving his money HK$2000 per month in a
regular savings account of HSBC which offers him interest rate of
4%p.a. compound monthly.
A bank teller suggest him to setup a monthly saving
plan. The details are as follow
Maturity of 5 years
Fixed interest rate 8%p.a. compound
quarterly
A handling fee equivalent to 2% of the total
investment amount for early withdrawal
If he needs to use the money 4 years from now, should
he take the offer?
First, find a Nominal yearly rate for monthly compounding
Annual effective rate if quarterly compounding = (1 + (r/4) )4-1 = (1 + (8/2)4-1 = (1+0.02) 4-1 = 1.0824 - 1 = 0.0824 = 8.24%
Annual Nominal rate for Monthly cmpounding = [(1+ EAR) 1/12 - 1] * 12 = [(1+0.0824)0.0833-1] *12 = [1.006620 - 1] *12 = 0.006620 * 12 = 0.0794 = 7.94%
Now use a financial calculator or excel for investment calculation
in Financial calculator
N = 12*4 = 48 is No of Month
I/Y = 7.94 / 12 = 0.6616 = monthly interest rate
PMT = - 2000 = monthly investment
PV = 0 = pesent value
FV = find = 112561.27 = Futur value of investment
Or use excel
=FV(rate,nper,pmt,pv,type) =FV(0.6616%,48,-$2000,0,0) = $112559.4
where,
nper = 12*4 = 48 is No of Month
rate = 7.94 / 12 = 0.6616 = monthly interest rate
PMT = - 2000 = monthly investment
PV = 0 = pesent value
type =0 = Ending mode
FV = find = 112561.27 = Futur value of investment
Here He withdraws early investment so He needs to pay 2% Handling equivalent
Value get after fee = Future Investment value - Fees = $112561.27 - ($112561.27*0.02) = $112561.27 -$2251.23 = $1110310.04
Following he will get from regular Investment
n Financial calculator
N = 12*4 = 48 is No of Month
I/Y = 4 / 12 = 0.3333 = monthly interest rate
PMT = - 2000 = monthly investment
PV = 0 = pesent value
FV = find = 103919 = Futur value of investment
Or use excel
=FV(rate,nper,pmt,pv,type) =FV(0.3333%,48,-$2000,0,0) = $ 103918.37
where,
nper = 12*4 = 48 is No of Month
rate = 4 / 12 = 0.3333 = monthly interest rate
PMT = - 2000 = monthly investment
PV = 0 = pesent value
type =0 = Ending mode
FV = find = 103918.37 = Futur value of investment
NOTE: Here we assume monthly investment at the end of the month, Answer can be different if Investment made at the beginning of the year
Hence
From Monthly saving plan, he will get $110310.04
From Regular saving, he will get $103918.37
He should take the offer because he will get $6391.67 more than the regular offer.
Question 2 Ho is now saving his money HK$2000 per month in a regular savings account...
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