How long (in years) will it take to triple your money if it is invested in a certificate of deposit (CD) that pays 3% annual interest compounded daily? Round to the nearest tenth of a year.

Question

How long (in years) will it take to triple your money if it is invested in a certificate of deposit (CD) that pays 3% annual interest compounded daily? Round to the nearest tenth of a year. (Use 365 days for each year.)

Answer 1

A = P(1+r/n)^nt

A/P = 3 means the investment is tripled

n = number of compounding periods per year

t= years

r = annual interest rate

plug in the values

A/P = 3 = (1+.03/365)^365t, solve for t

take logs to the base 1+.03/365

log_(1+.03/365)3 = 365t

365t = ln3/ln(1+.03/365)

t = ln3/365ln(1+.03/365)

use a calculator

= about 36.62 years

check the answer by assuming it's continuously compounded, answer is very close to the same as for daily compounding

3 = e^rt

ln3 = .03t

t = ln3/.03 = about 36.62

which is the same rounded to 2 decimal places

or for one decimal place

= 36.6 years