An accountant decided to open an IRA for her retirement. She planned to deposit $5,000 at the end of the first year. Then she planned to skip the payment for the 2nd year and make the $5,000 deposit every other year. In other words, she deposits her $5,000 every 2nd. year, so that in 30 years she will have made a total of 15 deposit. If she is able to earn 6% compounded annually, what would the balance in her IRA be in 30 years?
Thanks for any help.
+118659 An accountant decided to open an IRA for her retirement. She planned to deposit $5,000 at the end of the first year. Then she planned to skip the payment for the 2nd year and make the $5,000 deposit every other year. In other words, she deposits her $5,000 every 2nd. year, so that in 30 years she will have made a total of 15 deposit. If she is able to earn 6% compounded annually, what would the balance in her IRA be in 30 years?
Thanks for any help.
deposits end of 1{,3,5,7,9,11,13,15,17,19,21,23,25,27, 29}. yes that is 15 deposits
6% annually = is what in 24 months?
\((1+0.06)^2=(1+x)^1\\ 1.06^2-1=x\\ x=0.1236=12.36\% \;\;every \;\;2\;\; years \)
I think I will add in the first payment later. So I am starting at the end of year 1 but not including the first payment.
So I am going to start just after the 1st payment is mad at the end of year 1 and finish just after the 15th deposit is made at the end of year 29.
So I will have to add the last years interest later too.
So that is (14 deposits made at the end of each 2 years + the first year will be invested for 28 years,) then the amount that totals will be invested for 1 more year.
14 deposits made at the end of each 2 years=
\(5000*\frac{(1.1236^{14}-1)}{0.1236}\)
1 deposit is in the bank for 28 years will grow to 5000*0.0628
So I think the answer is ((5000*(1.1236^14-1)/0.1236)+5000*1.06^28)*1.06 = $203,402.13
That seems like an awful lot but it could be correct.
If you used a formua for future value of an anuity due formula it would be easier but not everyone is supposed to use that formula.
Very good work Melody. It is basically an ordinary FV of 15 payments @ 6% compounded annually, or 12.36% compounded biennially. The FV will be to the end of the 29th year and you would simply add 6% to the total for the last year. Or:
FV=P{[1 + R]^N - 1/ R}=FV OF $1 PER PERIOD.
FV=5,000{[1.1236]^15 -1 /0.1236}
FV=$191,888.80 X 1.06 =$203,402.13
