John Roberts has $42,180.53 in a brokerage account, and he plans to contribute an addtional $5,000.00 to the account at the end of the year. the brokerage account has an expected annual return of 12%. If John's goal is to accumulate $250,000.00 in the account, how many years will it take John to reach his goal?
An Excel spreadsheet is very good for these types of problems.
It may help if I knew how to do the equation.
In year 0, he has B0=42,180.53
In year 1, he has B1=B0*1.12 + 5000.
In year 2, he has B2=B1*1.12 + 5000.
Continue until Bn >= 250000.
To determine how many years it will take John to reach his goal of $250,000.00 in his brokerage account, we can use the concept of compound interest. Compound interest calculates the growth of an investment by taking into account the initial amount, any additional contributions, the annual interest rate, and the time period.
In this case, John's initial amount is $42,180.53, and he plans to contribute an additional $5,000.00 at the end of each year. The expected annual return on his brokerage account is 12%, which we convert to a decimal as 0.12.
Now, let's calculate the number of years it will take John to reach his goal using the following formula:
A = P * (1 + r)^n
Where:
A = the future value of the investment (goal amount)
P = the initial amount (current balance)
r = the annual interest rate
n = the number of compounding periods
In this case, we can rearrange the formula to solve for n:
n = log(A / P) / log(1 + r)
Substituting the given values:
n = log(250,000 / 42,180.53) / log(1 + 0.12)
Now, let's calculate it:
n = log(5.936) / log(1.12)
n ≈ 10.9
It will take approximately 10.9 years for John to reach his goal of $250,000.00 in his brokerage account.