How long will it take 100 to double if it earns the followin

How long will it take $100 to double if it earns the following rates? Compounding occurs once a year. Round each answer to two decimal places. A. 5% b. 14% c. 20% d. 100%

Solution

A.

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

A= P ( 1+ 5/100) ^ n

P = $ 100

Hence, A= 2 * $100

= $ 200

Hence, 200 = 100*(1+5/100) ^n

or 2 = (1.05) ^ n

Taking log on both sides we get,

log 2 = n log (1.05)

Hence, n = Log 2 / log (1.05)

or n = 14.20669908

= 14.21 Years

Hence the correct answer is 14.21 years.

B.

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

A= P ( 1+ 14/100) ^ n

P = $ 100

Hence, A= 2 * $100

= $ 200

Hence, 200 = 100*(1+14/100) ^n

or 2 = (1.14) ^ n

Taking log on both sides we get,

log 2 = n log (1.14)

Hence, n = Log 2 / log (1.14)

or n = 5.290058556

= 5.29 years

Hence the correct answer is 5.29 years.

C.

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

A= P ( 1+ 20/100) ^ n

P = $ 100

Hence, A= 2 * $100

= $ 200

Hence, 200 = 100*(1+5/100) ^n

or 2 = (1.2) ^ n

Taking log on both sides we get,

log 2 = n log (1.2)

Hence, n = Log 2 / log (1.2)

or n = 3.801784017

= 3.80 Years

Hence the correct answer is 3.80 years.

D.

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

A= P ( 1+ 100/100) ^ n

P = $ 100

Hence, A= 2 * $100

= $ 200

Hence, 200 = 100*(1+100/100) ^n

or 2 = (2) ^ n

Taking log on both sides we get,

log 2 = n log (2)

Hence, n = Log 2 / log (2)

or n = 1

= 1.00 years

Hence the correct answer is 1.00 years.