Question

How long will it take $500 to double if it earns the following rates? Compounding occurs once a year. Round each answer to two decimal places.

8%.

9%.

20%.

100%.

Answer 1

1)

8%:

Present value = 1

Future value = 2

Future value = Present value ( 1 + r)ⁿ

2 = 1 ( 1 + 0.08)ⁿ

2 = 1.08ⁿ

LN 2 = n LN 1.08

0.693147 = n 0.076961

n = 9.01 years

2)

9%:

Present value = 1

Future value = 2

Future value = Present value ( 1 + r)ⁿ

2 = 1 ( 1 + 0.09)ⁿ

2 = 1.09ⁿ

LN 2 = n LN 1.09

0.693147 = n 0.086178

n = 8.04 years

3)

20%:

Present value = 1

Future value = 2

Future value = Present value ( 1 + r)ⁿ

2 = 1 ( 1 + 0.2)ⁿ

2 = 1.2ⁿ

LN 2 = n LN 1.2

0.693147 = n 0.182322

n = 3.80 years

4)

100%:

Present value = 1

Future value = 2

Future value = Present value ( 1 + r)ⁿ

2 = 1 ( 1 + 1)ⁿ

2 = 2ⁿ

LN 2 = n LN 2

0.693147 = n 0.693147

n = 1 year