Candice deposited $3,587.39 into a savings account with an interest rate of 4.2% compounded twice a year. About how long will it take for the account to be worth $5,000?

8 years, 0 months

16 years, 7 month

8 years, 1 month

9 years, 10 months

Question

Candice deposited $3,587.39 into a savings account with an interest rate of 4.2% compounded twice a year. About how long will it take for the account to be worth $5,000?

 8 years, 0 months

 16 years, 7 month

 8 years, 1 month

 9 years, 10 months

hero · Answer

Semi-Annual Compounding Formula

$A = P\left(1 + \frac{r}{2}\right)^{2t}$

hero · Answer

A = 5000
P = 3587.39
r = .042

$5000 = 3587.39\left(1 + \frac{.042}{2}\right)^{2t}$

Solve for $t$

anonymous · Answer

I got 0

anonymous · Answer

help me please

anonymous · Answer

@agent0smith

agent0smith · Answer

$$\Large 5000 = 3587.39\left(1 + \frac{.042}{2}\right)^{2t}$$
first divide both sides by 3587.39

do you know how to take logs of both sides?

agent0smith · Answer

After dividing both sides by 3587.39 $$\Large 1.39377= \left(1 + \frac{.042}{2}\right)^{2t}$$now you have to take logs of both sides