Question

You currently have $4,400 (Present Value) in an account that has an interest rate of 8% per year compounded annually (1 times per year). You want to withdraw all your money when it reaches $6,600 (Future Value). In how many years will you be able to withdraw all your money?

Answer 1

Answer:

It will take 6 whole years to be able to withdraw all the money

Explanation:

To calculate the number of years it will take for the present value in your account to reach the future value we can adopt the expression below;

FV = PV (1 + r/n)^(nt)

where;

FV = the future value of the initial investment

PV = Present value of the initial investment

r = the annual interest rate

n = the number of times that interest is compounded per unit t

t = the time the money is invested for

In our case;

FV=$6,600

PV=$4,400

r=8/100=0.08

n=interest is compounded annually which is once a year=1

t=unknown

Replacing values in the formula;

6,600=4,400(1+0.08/1)^(1×t)

6,600=4,400(1+0.08)^t

6,600=4,400(1.08)^t

1.08^t=6,600/4,400

1.08^t=1.5

ln 1.08^t=ln 1.5

t×ln 1.08=ln 1.5

t=(ln 1.5)/ln 1.08

t=5.3 years

It will take 6 whole years to be able to withdraw all the money