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P Take a Test Alexis Gregory Google Chrome https://www.mathxl.com/Student/PlayerTest aspx?testld-142952845&centerwin; yes Fall16 College Algebra Trigsted 3e (1) Quiz: Quiz 4 (5.1-5.5) This Question: 1 pt 15 of 20 13 complete) Jimmy invests $22,000 in an account that pays 5.19% compounded quarterly How long (in years and months) wil it take for his investment to reach s25.000? years and months (Round the answer for months up to the nearest multiple of three) Enter Mour answer in each of the answer boxes,

Solution

The formula for compound interest is F = P(1+r/n)^nt , where P is the initial amount invested/principal, F is the maturity amount, r is the rate of interest for the period, n is the number of times that the interest is compounded in an year and t is the number of years. Here, P = $ 22000, F = $25000, r = (5.19/100)*1/4 = 5.19/400. Let t be the required numvber of years.Then, 25000= 22000( 1+5.19/400)^4t or, (405.19/400)^4t =25000/22000 =25/22. On taking logarithm of both sides, we get 4t log (405.19/400)= log (25/22) or,     0.0055987272* 4t = 0.055517327 so that t = 0.055517327/4*0.0055987272 = 2.479 years( approx) = 2years, 5.75 months = 2 years, 6 months (approximately).