Question

Manuel Rios wishes to determine how long it will take an initial deposit of ​$13 comma 000 to double. a. If Manuel earns 9​% annual interest on the​ deposit, how long will it take for him to double his​ money? b. How long will it take if he earns only 6​% annual​ interest? c. How long will it take if he can earn 11​% annual​ interest? d. Reviewing your findings in parts a​, b​, and c​, indicate what relationship exists between the interest rate and the amount of time it will take Manuel to double his money.

Answer 1

Answer:

See Below

Explanation:

This is a problem of compound interest. The formula is:

$F=P(1+r)^t$

Where

F is the future value

P is the present value

r is the rate of interest

t is the time in years

P = 13,000

To double his money, that means, F = 26,000

a)

Now, r = 9% = 0.09, so time it takes:

$F=P(1+r)^t\\26,000=13,000(1+0.09)^t\\2=1.09^{t}\\t=\frac{Ln(2)}{Ln(1.09)}\\t=8.04$

So, its gonna take about 8.04 years to double

b)

Similarly, here we just use r = 0.06, so the calculation is:

$F=P(1+r)^t\\2=1.06^t\\t=11.9$

So, its gonna take about 11.9 years to double

c)

Here, the r is 11% or 0.11

So, the time it will take:

$F=P(1+r)^t\\2 = 1.11^t\\t=6.6$

So, it is going to take about 6.6 years to double

d)

The amount of time it takes to double his money decreases as the interest rate increases and the time increases as interest rate decreases.