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?

Answer 1

9000= 4,190.51 * 1.052^n where n = 6 months
ln 9000 = ln (4,190.51 * 1.052^n)
ln 9000 = ln 4,190.51 + ln 1.052^n
ln 9000 - ln 4,190.51 = n ln 1.052
(ln 9000 - ln 4,190.51) / ln 1.052) = n

n is about 15.08. but n is 6 months so to convert to years multiply by 2
2n = 30.16 years

so it will take 30.16 years compounded twice a year at 5.2% interest.

Answer 2

I'm pretty sure 5.2% compounded twice a year means 5.2% for the whole year, or 2.6% every 6 months.

Answer 3

it should be 15.08/2 to go from months to years, I messed up.

whatever it is, just use ln to figure out the problem.

Answer 4

What is the answer?