Question

Assumed that a 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.

Peter 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.

Ten years later, Peter 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.

Another 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 18^th 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 the calculation)

Given the amount of the monthly instalment is $27729.87989.

No more information has given by the question.

Answer 1

Present Value of Education Fund target	$        580,000
Rate of return	4%
Tenure of Fund	18 Years
Annual Savings	$10,000
Increase in savings per year after Year 1	$5,000

CALCULATION OF PRESENT VALUE OF FUND IF THE SAVINGS ARE MADE AS PER QUESTION:

Year	Savings	Present Value
1	10,000	19,479.0050
2	15,000	28,094.7187
3	20,000	36,018.8701
4	25,000	43,291.9112
5	30,000	49,952.2052
6	35,000	56,036.1276
7	40,000	61,578.1623
8	45,000	66,610.9928
9	50,000	71,165.5906
10	55,000	75,271.2978
11	60,000	78,955.9068
12	65,000	82,245.7362
13	70,000	85,165.7032
14	75,000	87,739.3920
15	80,000	89,989.1200
16	85,000	91,936.0000
17	90,000	93,600.0000
18	95,000	95,000.0000
		1,212,130.7394

Formula to compute Present Value of Savings today:

where, n = Number of years for which Interest will be earned

Therefore, it can be concluded that the Target of Peter is achievable.