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?