Question

Problem 5-7 Calculating the Number of Periods [LO4]

At 7 percent interest, how long does it take to double your money? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

At 7 percent interest, how long does it take to quadruple it? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

a. The time period is computed as follows:

Future value = Present value x (1 + r)ⁿ

2 = 1 x (1 + 0.07)ⁿ

2 = 1.07ⁿ

Take log on both sides, we shall get:

log 2 = n log 1.07

0.693147181 = n x 0.067658648

n = 0.693147181 / 0.067658648

n = 10.24 years Approximately

b. The time period is computed as follows:

Future value = Present value x (1 + r)ⁿ

4 = 1 x (1 + 0.07)ⁿ

4 = 1.07ⁿ

Take log on both sides, we shall get:

log 4 = n log 1.07

1.386294361 = n x 0.067658648

n = 1.386294361 / 0.067658648

n = 20.49 years Approximately