A.. You have the following information. In 12 years and in 15 years you will sen

Question

A.. You have the following information. In 12 years and in 15 years you will send your two nephews to attend school. The tuition now is $8,000 but will grow at 2% per annum. The school will guarantee the tuition to be the same per year at the time your nephews enroll, but you need to address the rise of the tuition before that time. You want to take care of your father’s nursing home in 4 years which costs $100,000 yearly now, but will increase at a rate of 4% yearly. The nursing home will charge an expense which will remain fixed per annum for the duration of the convalescence which will be 30 years. That expense , now, is $40,000. You will retire in 50 years and be in retirement 15 years. You will need $90,000 of income annually. If you can borrow or lend at 7% interest rate, how much should you save per year in the next 50 years, in order to finance the aforementioned?

Explanation / Answer

Monetary requirements:

Tution fees:

To calculate the total expense for tutrion, we need to use the future value formula as shown below:

FV = PV(1+i)n

Where,

PV = Present value or current value

i = Interest rate

n = Number of years

After 10 years, the tuition fees of the first nephew is

= $8,000*(1+0.02)^10

= $9,751.955

After 15 years, the tuition fees of the second nephew is

= $8,000*(1+0.02)^15

= $10,766.95

Therefore, the total expense for both nephews' tuituion fees for 12 years = ($9,751.955 + $10,766.95)*12

= $246,226.86

Nursing home:

At 4% inflation, the cost of running nursing home after 4 years would be = $100,000*(1+0.04)^4

= $116,985.856 per year

So the total cost during 30 years of time = $116,985.856*30 years

= $3,509,575.68

Expenses for a retirement period of 15 years = $90,000*15 years

= $1,350,000

Total moneotry requirements = $246,226.86 + $3,509,575.68 + $1,350,000

= $5,105,802.54

So $5,105,802.54 should be the future value of annuity (FVA) after 50 years at 7% of interest rate. Now calculate the requirements per year savings by using the formula for annuity iis as follows:

FVA40 = R*(FVIFA7%,50)

Where,

FIFA = future value interest factor of annuuity

R = Savings per year

or $5,105,802.54 = R*((1+0.07)^50-1))/0.07

or $5,105,802.54 = R*(29.45702506-1)/0.07

or $5,105,802.54 = R*406.5289

or R = $12,559.51

Therefore, total amount of $12,559.51is required to save per each year for next 50 years in order to bear all the expenses.

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