need help withHow long will it take to double your money if

need help with....How long will it take to double your money if it is invested in a certificate of deposit that pays 2.0% annual interest compounded daily? Round to the nearest tenth of a year. Thank you, Austin Clayton, austincl2017@paragouldschools.net

Solution

The formula for compound interest is F = P(1+r/n)nt, where F is the future value, P is the principal,/initial amount, r is the rate of interest in decimals , n is the number of times the interest is compounded in an year and t is the number of years. Here, F = 2P, r = 2/100 and n=365.Let the money get doubled in t years. Then 2P=P[1+2/36500]^365t or, 2=(36502/36500)^365t = (1.000054795)^365t. Now, on taking logarithm of both the sides, we get log2 = 365t log( 1.000054795 ) or, 0.301029995 = 365t(0.00002379651418). Hence t = 0.301029995/(365*0.00002379651418) = 0.301029995/0.008685727675 = 34.658 years or, 34.7 years (on rounding off to the tenth of an year)