7 Solve by hand How long would it take for 12000 to double i

7.) Solve by hand. How long would it take for $12,000 to double in value (be worth $24,000) if it were invested in an account which pays 5.73% APR compounded semiannually. (If no work is shown, no credit will be given)

Solution

Principal =$12000 ;Amount = $24000 ; t = ? r = 5.73% = 0.0573

A = P( 1+r/n)^nt

n= 2 (semi - annually)

Plug all values:

24000 = 12000( 1+0.0573/2)^2*t

2 = (1.0573)^2t

taking natural log on both sides:

ln(2) = 2t*ln(1.0573)

t = 6.22 years to double the money