You want to buy a house in 4 years and expect to need $30,000 for a down payment. if you have $15,000 to invest, how much interest do you have to earn (compounded annually) to reach your goal? a. 21.53% b. 16.67% c. 13.62% d. 18.92%

The amount you desire, 30,000 is double (2 times) the amount you have, 15,000.

If r is the annual interest rate, the annual multiplier is (1+r). After 4 years, you want the multiplier to be 2, so the relationship is

... 2 = (1+r)⁴

... r = 2^(1/4) - 1 . . . . solve for r

... r ≈ 0.1892 = 18.92% . . . . matches selection d.

You can estimate this using the "rule of 72", which says the product of interest rate and doubling time (years) is about 72. That is, the rate will be about 72/4 = 18 percent.

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