1400 dollars is placed in an account with an annual interest rate of 7.75%. To the nearest tenth of a year, how long will it take for the account value to reach 6400 dollars?

It'll take 20.36 years to reach that value.

Step-by-step explanation:

In order to find the time it'll take to achieve the final value, we need to apply the compounded interest formulla shown below:

M = C * (1 + r) ^t

Where M is the final value, C is the initial value, r is the interest rate and t is the time elapsed. Applying the data from the problem in the equation, we have:

6400 = 1400 * (1 + 0.0775) ^t

6400 = 1400 * (1.0775) ^t

(1.0775) ^t = 6400/1400

(1.0775) ^t = 4.5714

ln (1.0775^t) = ln (4.5714)

t = ln (4.5714) / ln (1.0775)

t = 20.361

It'll take 20.36 years to reach that value.

46 years 1 month

Step-by-step explanation:

Let us assume the investment is a simple interest investment

The simple interest formula is

A = P (1+rt)

Given

Principal p = $1400

Rate r = 7.75% = 7. 75/100 = 0.0775

Final amount A = $6400

Time t=?

To find the time t let us substitute our values in the simple interest formula

6400 = 1400 (1+0.0775t)

6400 = 1400+108.5t

6400-1400=108.5t

5000 = 108.5t

t=5000/108.5 = 46.08

t = 46.1 years

It will take approximately 46 years 1 month to get the amount