Question

Question 1
Benjamin, a software engineer, would like to invest in an attractive fund sold by a bank. The
fund is to buy the stock of Big Bang Company. It is assumed that the fund can pay dividend
steadily for the coming 10 years, which will generate an equivalent return of 5% annually, and
the bank charge is negligible. He is thinking of investing ($10,000 ) at the end of
each month in this fund for the purpose of using it for the down payment of purchasing a real
property in the future.
(a) How much down payment would he have accumulated at the end of 10th
year? (Use 4
decimal places of the interest rate factor to do your calculation and round off your final
answer to integer.)

(b) Ten years later, he gets married. Although the fund value has increased a lot and became
sufficient for him to pay for the down payment of purchasing a residential property, they
still have to borrow ($5,000,000 ) from a bank. They select a 20 years
mortgage plan at 3% annual interest rate.
What is the amount of their monthly instalment? (Use 4 decimal places of the interest
rate factor to do your calculation and round off your final answer to integer.)

(c) Several years later, they bear a child. They plan to join an education fund today with a
guarantee return of 4% annually. Their target is $580,000 (in today dollar value) to be
redeemed at the end of 18th year. They plan to save ($10,000 ) at the end of
each year and increase by ($5,000 ) each year starting from Year 2.
Can their target be achievable? Show detailed steps of your analysis. (Use 4 decimal
places of the interest rate factor to do your calculation and round off your final answer to
integer.)

With clear Steps thanks

Answer 1

Formulas Used

1.

Step1. Calculation of future value of annuity.

Investment Amount	=10,000
Dividend Interest(Monthly)(5%/12)	=0.004166667
Total Time((10*12)-1)	=119 (Refer Step 2)
Future Value Factor of annuity	=((1+r)^n-1)/r
where r = rate, n = total time.	=((1.004166667)^119 - 1)/004166667
	=(1.640175 + 1)/004166667
	=153.6421
Future Value of annuity	=FV Factor*Annuity
	=153.6421*10000
	=15,36,421

Step 2. Since, the payments made are at the end of the year, interest will not be paid on the last payment and hence 119 is considered as total time period for the calculation of future value on the annuity. We shall add the last month's $10,000 to find the final answer.

Hence the future value of the investment = 1,536,421 + 10,000 = $1,546,421

2.

Loan Amount	5000000
Time Period(Monthly)(20*12)	240
Interest Rate(3%/12)	0.0025
Present Value Factor	(1-(1+r)^n)/r
where r= interest, n = time period
	(1-(1+0.0025)^-20)/0.0025
	(1-0.450777)/0.0025
	180.3109
Monthly Payment	Loan Amount/PVF
	5,000,000/19.4844
	$27,729.88
Or USING PMT function in excel
Monthly Payment	$27,729.88

Hence, the monthly payments are $27,729.88

3.

Every year their is an increase of $5000 in the investment. If they invest $10,000 today, 2nd year it will be $15,000, 3rd year it wil be $20,000. We shale make a table a find a future value factor for each year and multiply it by the respective amounts. We will sum all these to find the aggregated value.

Clearly, the amount accumulated is greater than the requried amount i.e $580,000. The amount accumulated is $1,260,623.00.

Hence, they should go for the investment

If you have any doubt, ask me in the comment section please.