Question

Biswaroop wants to take a year long vacation in Thailand. He figures he can live on 41200 bhat per month. (1 Canadian dollar = 36 Thai bhat (rougly)). He plans to withdraw that amount at the start of each month from his Thai savings account paying 3% interest compounded monthly.

a) How much money (in Thai bhat) will he need in his Thai account at the start of his vacation? In order to save up the necessary amount of money, Biswaroop will deposit money at the end of each month for 3 years in a Canadian savings account paying 2% per year compounded monthly. His first deposit will be $P and then each subsequent deposit will increase by $P.

b) How much does he need in Canadian dollars so that when he transfers it to his Thai account he has enough bhat for the year?

c) What is the PV of an annuity due paying $1 (Canadian) per month for 12 months?

d) How big does $P have to be so that he ends up with enough Canadian dollars in his account to start his vacation?

Answer 1

Answers:

a.) ฿ 487,675

b.) $13,546.53

c.) $11.89

d.) $44.58

Explanation:

a.) Her we want to find the present value of the amount at the beginning of the year.

Annual rate = 3%. So, monthly rate = 2%/12 = 0.0025% per month.

We can calculate the present value in excel using inbuilt function 'PV'

Please find the attached image for detailed solution with excel formula

b.) 1 Canadian dollar = 36 baht

So, ฿ 487,675 / 36 = Canadian $13,546.53

.

c.) Present value of annuity due can be derived as...

PV of annuity due = P + P [ {1 - {(1+r)^-(n-1)} } / r ]

Where P = Periodic payment = $1, r = Rate per period = 2/12 = 0.1667%, n = number of period = 12

PV of annuity due = 1 + 1 [ { 1 - { (1.001667)^(-11)}}/0.001667]

= 1 + 1 [ { 1 - 0.9818 } / 0.001667 ]

= 1 + 1 [ 10.89]

= $11.89

d.) Future value of this arithmetically increasing annuity should be $13,546.53

Interest rate = 2%/12 = 0.1667% per month, Number of periods = 24 and FV = $13,546.53

.

To simplify this let's calculate Future value of $1 arithmetically increasing over the period of 2 years.

Please find the attached image for the calculation of FV of arithmetically increasing annuity.

Here FV = Payment * { (1+interest)^(24-month)

So, $P invested in first month becomes $303.87 P at the end of 24 months.

So, $13,546.53 / 303.87 = $44.58

So, Value of P = $44.58

.

Hope this helps. let me know if you need further clarification in any of the step(s).

All the best!