Question

An investment offers to double your money in 30 months (don’t believe it). What rate per six months are you being offered? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

14.86% every 6 months

Explanation:

Let the original amount be a

An investment offers to double your money in 30 months i.e. 2a in 30 months

Fv = Pv (1 + x)ⁿ

Fv future value (i.e. future value of the cash flow after a particular time period. )

Pv Present value

x interest

n number of compounding period

Fv = Pv (1 + x)ⁿ

2a = a (1 + x)^(30/6)

2^(1/5)= 1 + x

1.1486 = 1 + x

x = 0.1486 0r 14.86%

Answer 2

Answer:

The rate of change in 6 months is 14.87%

Explanation:

Let a be the amount that the money is multiplied in one month. We know that in 30 months it is multiplied by 2, so if we power a by 30 wew obtain 2:

a³⁰ = 2

Thus, 2 = a³⁰ = a⁶*⁵ = (a⁶)⁵

(here we use the propiety a^bc = (a^b)^c = (a^c)^b)

We can conclude that a⁶ = 2^(1/5) = 1.1487

The rate in 6 months is (1.1487-1)*100 = 14.87%