How much time will be needed for 29000 to grow to 36 972 if

How much time will be needed for $29,000 to grow to $36, 972 if deposited at 7% compounded quarterly? For calculating use the formula A = P [1 + r/k]^kl The amount $29,000 will grow to $36, 972.59 in years. (Do not round until the final answer. Then round to the nearest tenth as needed.)

Solution

Let the time required for $ 29000 to grow to $ 36972.59, when deposited at 7 % interest compounded quarterly be t years. Then, we have 36972.59 = 29000[ 1+0.07/4]^4t or, (4.07/4)^4t = 36972.59 / 29000 = 1.274916897. Now, on taking logarithm of both the sides, we get 4t log (4.07/4) = log(1.274916897) or, 4t(log 4.07-log4) = log (1.274916897) so that t = log (1.274916897) /4(log 4.07-log4) = 0.105481877/4*( 0.609594409-0.602059991) = 0.105481877/ 4*0.007534418 =0.105481877/0.030137672 = 3.5 years. Thus, it will take3.5 years for $ 29000 to grow to $ 36972.59, when deposited at 7 % interest compounded quarterly.