Find how many years it will take for 15500 to increase to 30

Find how many years it will take for $15,500 to increase to $30,000 in a saving account with a 6.75 % interest rate with 4 compounding yearly A +P(1+r/n)^nt

Solution

principal, P = $15,500

amount , A = $ 30,000

rate , r = 6.75% ; n =4

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

30,000 = 15,500( 1 + 0.0675/4)^4t

1.935 = 1.0675^4t

take log on both sides: ln(1.935) = 4t*ln(1.0675)

t = 2.526 years