Question

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?

Answer 1

46 years 1 month

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

Answer 2

It'll take 20.36 years to reach that value.

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.