You have the following information. In 10 years and in 15 years you will send yo

Question

You have the following information. In 10 years and in 15 years you will send your two nephews to attend school. The tuition now is $10,000 but will grow at 7% 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 40 years which costs $40,000 yearly now, but will increase at a rate of 6% yearly. The nursing home will charge an expense which will remain fixed per annum for the duration of the convalescence which will be 20 years. You will retire in 40 years and be in retirement 35 years. You will need $60,000 of income annually. If you can borrow or lend at 5% interest rate, how much should you save per year in the next 40 years, in order to finance the aforementioned?

Explanation / Answer

Total Monetary Requirements are as follows:

1. Tuition Fee

Using the future value formula FV= PV(1+i)n, where PV = present value, i= interest rate and n = no. of years

After 10 years the tuition fee for the first nephew would be = 10000*(1+0.07)10= $19671.51 per annum

similarly the tuition fee for second nephew after 15 years would be = 10000*(1+0.07)15=$27590.32 per annum

So total expense for schooling for 12 years for both nephews would be = (19671.51+27590.32)*12 = $567141.9

2. Nursing Home

At 6% inflation the cost of running nursing home after 40 years would be = 40000*(1+0.06)^40 = $411428.7 p.a.

Hence the total cost during 20 year period = 411428.7*20 = $8228574

3. Expenses during retirement period of 35 years = 60000*35 = $2100000

Adding the above we get the total monetary requirements = 567141.9+8228574+2100000 =$10895716

Hence $10895716 should be the future value of annuity (FVA) after 40 years at 5% interest rate. Using the formula for annuity the required per year savings would be-

FVA40 = R*(FVIFA5%,40), where FVIFA is future value interest factor of annuity and R is periodic savings.

or 10895716 = R* ((1+0.05)^40-1))/0.05

or 10895716 = R* (7.039989-1)/0.05

or 10895716 = R*120.7998

or R = $90196.5

Hence  $90196.5 per annum is needed to be saved per annum for next 40 years to finance the aforementioned expenses.

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