John Roberts has Rs.42,108.53 in a brokerage account, and he plans to contribute an additional Rs. 5,000 to the account at the end of every year. The brokerage account has an expected annual return of 12%. If John's goal is to accumulate Rs. 250,000 in the account, how many years will it take for John to reach his goal?

Question

John Roberts has Rs.42,108.53 in a brokerage account, and he plans to contribute an additional Rs. 5,000 to the account at the end of every year. The brokerage account has an expected annual return of 12%. If John's goal is to accumulate Rs. 250,000 in the account, how many years will it take for John to reach his goal?

Answer 1

An investment pays Rs20 semiannually for the next 2 years. The investment has a 7% nominal interest rate, and interest is compounded quarterly. What is the future value of the investment?

Answer 2

#1

let the number of years be n
42,108.53(1.12)^n + 5000(1.12^n - 1)/.12 = 250,000
nasty arithmetic steps ahead:
multiply each of the 3 terms by .12
expand the second term
isolate terms containing 1.12^n, then factor out 1.12^n
take logs of both sides and find n

I sent this through Wolfram and got n = 11.0076
or appr 11 years

https://www.wolframalpha.com/input/?i=solve+42%2C108.53%281.12%29%5Ex+%2B+5000%281.12%5Ex+-+1%29%2F.12+%3D+250%2C000

check:
42,108.53(1.12)^11 + 5000(1.12^11 - 1)/.12
= 249749.54

For your 2nd question, what is your effort so far?
Did you notice that the compounding period of the payment does not match the compounding period of the interest rate?
This stops us from using our regular formulas.
What do you think will be the most difficult part of the problem?

Answer 3

To find out how many years it will take for John to reach his goal of accumulating Rs. 250,000 in the brokerage account, we can use a formula for calculating the future value of an ordinary annuity:

FV = P * [(1 + r)^n - 1] / r

where:
FV is the future value
P is the periodic payment
r is the interest rate per period
n is the number of periods

In this case, John's initial investment of Rs. 42,108.53 is the future value of the first year's contribution, and he plans to contribute an additional Rs. 5,000 at the end of every year. The interest rate per period is 12%, and he wants to accumulate Rs. 250,000 in total.

Let's substitute these values into the formula and solve for n:

250,000 = (42,108.53 + 5,000) * [(1 + 0.12)^n - 1] / 0.12

Now, we can solve this equation for n using algebraic methods. Since it involves an exponential term, it may be challenging to solve it algebraically. Instead, it is easier to use trial and error or utilize a financial calculator or spreadsheet software.

Let's try using an iterative approach with a financial calculator or a spreadsheet:

1. Start with an initial guess for n, such as 10 years.
2. Calculate the future value using the formula above for the guessed value of n.
3. Compare the calculated future value with the desired value of Rs. 250,000.
4. If the calculated future value is lower than Rs. 250,000, increase the guess for n and repeat steps 2 and 3.
5. If the calculated future value is higher than Rs. 250,000, decrease the guess for n and repeat steps 2 and 3.
6. Continue adjusting the guess for n until the calculated future value is very close to Rs. 250,000.

By iterating through this process, you can find the approximate number of years it will take for John to reach his goal.