Question

Question 3:

You wish to save $2000 to go on a holiday when you finish university in 2.5 year’s time. You plan to do this by making regular deposits of the same size into a savings account that pays interest j52= 4.68% p.a., starting in one week’s time.

a) Illustrate this scenario as a fully labelled time line diagram.

b) Determine the deposit size required. Enter this value to 2 decimal places as an answer.

c) Explain and perform a sanity check on your answer to (b)

d) Immediately after your 50th deposit, the interest rate increases to j52=4.78 % p.a. Draw an appropriate time line of the scenario and then determine what deposit size will now be needed for deposits 51 to 130 in order to still meet your original target of $2000.

e) Determine how much will be accumulated at the end of the savings scheme if you continue with the old weekly deposit size after the interest rate changes

Answer 1

a)

Timeline	0	1	2	3	………..	130
Amount	0	X	X	X	X	X

X denotes the weekly equal payment to be made to get $2000 at the end of 2.5 years.

1 year = 52 weeks

2.5 = 52*2.5 = 130 weeks

b) Fv = $2000

Weekly rate (rate) = 4.68%/52

NPER = 130 (weeks)

Compute PMT, PMT = $14.51 Excel formula: =PMT(4.68%/52,130,0,-2000,0)

c)To cross check the answer,

FV = $2000

NPER = 130

Rate = 4.68%/52

Calculate PV = $1779.26 Excel formula: =PV(4.68%/52,130,0,-2000,0)

Rate = 4.68%/52

NPER = 130

PMT = $14.51

Calculate PV = $1779.26 Excel formula: =PV(4.68%/52,130,-14.51,0,0)

In both calculation PV is equal, Therefore the payment we have found out in previous step is correct.

d) First, the amount we will have at the end of the 50th payment must be f out.

Rate = 4.68%/52

NPER = 50

PMT = $14.51

Calculate FV = $741.68 Excel formula: =FV(4.68%/52,50,-14.51,0,0)

Then keeping this as PV, Calculate the payment,

PV = 741.68

NPER = 80

Rate = 4.78%/52

FV = 2000

Calculate PMT = $14.48 Excel Formula: =PMT(4.78%/52,80,-741.68,2000,0)

e) PV = 741.68 (Calculated in previous step)

PMT = 14.51

Rate = 4.78%/52

Compute FV = $2002.15 Excel Formula: =FV(4.78%/52,80,-14.51,-741.68,0)