Question

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?

Answer 1

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