Question

How long will it take $400 to double if it earns the following rates? Compounding occurs once a year. Round each answer to two decimal places. 5%. year(s) 14%. year(s) 20%. year(s) 100%. year(s)

Answer 1

Compound interest formula is

A = P*(1+r)^n

Here, A = 2P .. Given

Thus, 2 = (1+r)^n

Thus, n = log 2/ log (1+r)

When r = 5% i.e. 0.05

Thus, n = log 2/log 1.05

= 14.21 years

When r = 14% i.e. 0.14

Thus, n = log 2/log 1.14

= 5.29 years

When r = 20% i.e. 0.2

Thus, n = log 2/log 1.2

= 3.80 years

When r = 100% i.e. 1

Thus, n = log 2/log 2

= 1 year