Solve this application using logarithms.

At what interest rate (to the nearest hundredth of a percent) compounded annually will money in savings double in five years?

Solve this application using logarithms.

How much principal, to the nearest dollar, should you invest at 4% in order to have $3,000 for a vacation to Europe in 3 years?

Amount = P (1 + r) ^n

2P = P (1 + r) ^5

(1 + r) ^5 = 2

log (1 + r) ^5 = log 2

5 log (1 + r) = log 2

log (1 + r) = 1/5 log 2 = log 2^ (1/5)

1 + r = 2^ (1/5)

r = 2^ (1/5) - 1 = 1.1487 - 1 = 0.1487

Therefore, interest rate is 14.87%

3000 = P (1 + 0.04) ^3

log 3000 = log P (1.04) ^3

log 3000 = log P + log (1.04) ^3

log P = log 3000 - log (1.04) ^3

log P = log (3000 / (1.04) ^3) = log 2667

P = $2,667