Question

Ramona deposited $4,190.51 into a savings account with an interest rate of 5.2% compounded twice a year. About how long will it take for the account to be worth $9,000?

33 years, 5 months

29 years, 9 months

14 years, 11 months

20 years, 8 months
9,000=4,190.51(1+0.052/2)^2t
4,809.49= 1.026^2t

Answer 1

if we just let the exponent reference 6month time periods, we can ignore the 2 on it

Answer 2

A = P(1+r/2)^t

A/P = (1+r/2)^t

ln(A/P) = t ln((1+r/2))

ln(A/P)/ln(1+r/2) = t

and 1t is equal to 6 months, or half a year