1. Some time ago, Vanessa purchased eleven acres of land costing $58,500. Today,

Question

1. Some time ago, Vanessa purchased eleven acres of land costing $58,500. Today, that land is valued at $253,167. How long has she owned this land if the price of the land has been increasing at 9% per year?

2.. On your ninth birthday, you received $500 which you invested at 4% interest, compounded annually. Your investment is now worth $1,185. How old are you today?

3. Assume the total cost of a college education will be $200,000 when your child enters college in 15 years. You presently have $80,000 to invest. What rate of interest must you earn on your investment to cover the cost of your child's college education?

Explanation / Answer

Part 1

Let the period for which land was owned by x years

58500*(1.09)^x = 253167

Using trial and error method we get x = 17

Thus, he owned the land for 17 years

Part 2

Let the amount was deposited for x years

500*(1.04)^x = 1185

Using trial and error method we get x = 22 years

Thus, the age will be 9 + 22 = 31 years

Part 3

Amount available for investment = 80000

Amount required = 200,000

Investment Period = 15 years

Let the rate of return be r

80000*(1+r)^15 = 200000

r = (200000/80000)^(1/15)-1 = 6.3%

The rate of return is 6.30%

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