Question

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.

6%.= year(s)

9%.= year(s)

21%. = year(s)

100%= . year(s)

Answer 1

He wants to double the principal amount at diff int rates

If Int rate is 6%:

Amount = Principal ( 1 + r )ⁿ

where r is interest rate & n is no. of years

$ 200 = $ 100 ( 1 + 0.06 )ⁿ

2 = (1.06)ⁿ

Take Logarithm on both sides

Log 2 = n * Log 1.06

n = Log 2 / Log 1.06

= 0.3010 / 0.0253

= 11.90 years

If Int rate is 9%:

Amount = Principal ( 1 + r )ⁿ

where r is interest rate & n is no. of years

$ 200 = $ 100 ( 1 + 0.09 )ⁿ

2 = (1.09)ⁿ

Take Logarithm on both sides

Log 2 = n * Log 1.09

n = Log 2 / Log 1.09

= 0.3010 / 0.0374

= 8.05 years

If Int rate is 21%:

Amount = Principal ( 1 + r )ⁿ

where r is interest rate & n is no. of years

$ 200 = $ 100 ( 1 + 0.21 )ⁿ

2 = (1.21)ⁿ

Take Logarithm on both sides

Log 2 = n * Log 1.21

n = Log 2 / Log 1.21

= 0.3010 / 0.0828

= 3.64 years

If Int rate is 100%:

Amount = Principal ( 1 + r )ⁿ

where r is interest rate & n is no. of years

$ 200 = $ 100 ( 1 + 1 )ⁿ

2 = (2)ⁿ

2 = (2)¹

Thus n is 1 year