Jim Jones, an owner of a Burger King restaurant, assumes that his restaurant will need a new roof in 7 years; He estimates the roof will cost him $9,000 at that time. What amount should Jim invest today at 6% compounded quarterly to be able to pay for the roof? Check your answer.
Could someone help me figure this question out please.
Nov 24th 2005, 05:33 AM
The general formula used to express the amount, A, an investment will be worth when principal, P, is invested at interest rate, r, for time, t, with number of compoundings per year, n, is given as follows: A=P[1+r/n]^(nt). In the case at hand, we wish to know how much money must be invested if an AMOUNT OF $9,000 is desired at the end of a seven year period. Because the word 'principal' refers to the initial investment, it is 'P' that we seek to determine in the formula. A=9,000, r= 0.06 (always express the interest rate as a decimal), n=4 (quarterly compounding means the investment compounds every "quarter year", giving four compoundings per year), and t=7 (i.e., 7 years). Substituting the known values into our formula gives,
9,000 = P[1 + 0.06/4]^(4*7) which simplifies to 9,000 = P[1 + 0.015]^28 or, 9,000 = P[1.015]^28. Now we use a bit of algebra and divide both sides of the equation by [1.015]^28 which leaves P = 9,000/[1.015]^28. I leave the final calculations to you and your calculator. And there you have it!