Question

a savings account balance is compounded continuously. If the interest rate is 3.1% per year and the current balance is $1077.00, in how many years will the balance reach $1486.73

Answer 1

10.55 years

Explanation:

In order to calculate the number of years, you have to isolate N from the formula:

FV=PV*(1+I)^N

FV= Future value

PV= Present value

i= Interest rate

N= number of periods

FV/PV=(1+i)^N

ln(FV/PV)=Nln(1+i)

N=ln(FV/PV)/ln(1+i)

Now you have to replace the formula to find the answer:

FV= 1486.73

PV= 1077

i= 3.1%

N= ln(1486.73/1077)/ln(1+0.031)

N= ln(1.38)/ln(1.031)

N= 10.55

The answer is that it will take 10.55 years for the balance to reach $1486.73.