Problema Solution
Bonus. Joe wants to invest his inheritance of $20,000 into a savings account
and would like to double his money in 10 years. Assuming interest is compounded monthly,
what annual interest rate r will guarantee this return (express your answer as a percent to five
decimal places)?
Answer provided by our tutors
P = $20,000 is the principal
A = 2*P = $40,000 the future value since he wants to double his money
t = 10 years
m = 12 compounding periods per year since interest is compounded monthly
n = m*t = 12*10 = 120 compounding periods
i = r/m = r/12 interest rate per month
r = ? annual interest rate
A = P(1 + i)^n
40000 = 20000(1 + r/12)^120
(1 + r/12)^120 = 2
r = 0.0695152
r = 6.95152%
the annual rate that will guarantee the return is 6.95152%.