Question

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?

Answer 1

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.