Question

3. Suppose you are offered an investment that will allow you to double your money in 6 years. You have $20,000 to invest. What is the implied rate of interest? (r)

4. You want to purchase a new car, and you are willing to pay $20,000. If you can invest at 6% per year and you currently have $15,000, how long will it be before you have enough money to pay cash for the car? (t)

Answer 1

3)	Given that, the Investment will double in 6 Years
	Amount of Investment(P) = $ 20,000
	Amount after 6 Years = 2 * $ 20,000 = $ 40,000
	Implied Interest Rate = r
	Amount = P * (1+i)^n
	$ 40,000 = $ 20,000 * (1+r)^6
	$ 40,000 / $ 20,000 = (1+r)^6
	(1+r)^6 = 2
	(1+r) = 2^(1/6)
	1+r = 1.122462
	r = 1.122462 - 1
	r = 12.2462% = 12.25% (approx)

4)	Price of Car = $ 20,000
	Amount Currently available for Investment = $ 15,000
	Return on Investment = 6%
	Time Taken = t
	Amount = P * (1+i)^n
	$ 20,000 = $ 15,000 * (1+0.06)^t
	$ 20,000 / $ 15,000 = (1.06)^t
	1.3333 = (1.06)^t
	t = 5 Years (approx)