# If you put \$2,000 into an interest bearing account, where interest is compounded quarterly (4 times a year) at 6%, how long will it take for your money to triple?                      ...

If you put \$2,000 into an interest bearing account, where interest is compounded quarterly (4 times a year) at 6%, how long will it take for your money to triple?

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

Solve for t.

Enter ___ years to one decimal.

baxthum8 | High School Teacher | (Level 3) Associate Educator

Posted on

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

P(principal) = 2000;  r(rate) = 6% or 0.06; n(#of times compounded per year) = 4; A = amount after applying rate and time = \$6000 (2000 tripled) and t = amount of time = what we are trying to find.

`6000 = 2000(1 +(.06)/(4))^(4t)` ;  divide each side by 2000 and simplify parenthesis

`3 = ((203)/(200))^(4t)` ;  now take log of each side

`log 3 = log((203)/(200))^(4t)` therefore use power rule

`log 3 = 4t*log((203)/(200))`

divide each side by log(203/200)

73.789 = 4t  divide each side by 4

`t = 18.447`   one decimal place is:  `t = 18.4`