Question

(a) Rental costs for office space have been going up at 5% per year compounded
semiannually for the past 4 years. If office space rent is now RM40 per square
foot per month, what were the rental rates 4 years ago? [4 marks]

(b) Find the effective rate of interest corresponding to a nominal rate of 8% per year
compounded

(i) semiannually, [3 marks]

(ii) monthly. [3 marks]

(c) Sally wishes to accumulate a sum of $400,000 in a retirement account by the time
of her retirement 25 years from now. If she wishes to do this through monthly
payments into the account that earn interest at the rate of 6% per year
compounded monthly, what should be the size of each payment? [5 marks]

(d) John has RM50,000, 18 years mortgage at 7% compounded monthly.
(i) Find the monthly payment? [5 marks]

(ii) Suppose John decide to add an extra RM50 to his mortgage payment each
month starting from the very first payment. How long will it take John to
pay off the mortgage?[5 marks]

Answer 1

a. FV=PV*(1+r)^n

40=PV*(1+5%/2)^(4*2)

40= PV*1.218402898

PV=40/1.218402898= 32.82986283

Rates 4 years ago were $32.83 per sqft per month

B. Effective rate= (1+Nominal rate/n)^n-1

i)Semiannually compounded

Effective rate=(1+ 8%/2)^2-1= 8.16%

ii) Monthly compounded

Effective rate= (1+8%/12)^12-1= 8.3%

C. Future Value of annuity = A* ((1+rate)^n-1)/rate

400000=A*((1+6%/12)^(25*12)-1)/(6%/12)

400000= A*692.9939624

A= 400000/692.9939624

Size of each payment =$ 577.21

D: i)PV of annuity = Annuity*(1-1/(1+rate)^number of terms)/rate

50000=A*(1-1/(1+7%/12)^(18*12))/(7%/12)

50000= A*122.6238306

A=$407.75

ii) A=$407.75+50= $457.75

Using financial calculator

PMT= -457.75

PV= 50000

I/Y=7/12

Solve for N as 174.3057403

It will take 174.3057 months which is 14.53 years