Question

Helena deposited $89 into a savings account for which interest is compounded monthly. According to the Rule of 72, what interest rate will cause her money to double in approximately 38 years? A.2.3% B.1.9% C.0.4% D.0.5%

Answer 1

You have something like:
178 = 89 (1+i)^n
178 is 89 * 2 the double of money
i: interest by month
n: number of months
n=38*12=456
now you have:
178 = 89*(1+i)^456
178/89 = (1+i)^456
2=(1+i)^456
using Log:
Log(2) = 456*Log(1+i)
0.301 = 456*Log(1+i)
0.301/456 = Log(1+i)
using 10^x you get:
10^(0.301/456) = 1+i
solving for i you get i=0.152%
i by 12 = 1.825 compounded monthly aprox. ->1.9%