1. ## [SOLVED] Annuities

I am not sure what's the correct approach to this question. Can I get some guidance please??

As part of a retirement package for a local oil company, Jerry will receive $36,000 every 6 months for the next 20 years. If the funds to fund this pension are invested at a rate of $J_1 = 8 \%$, how much money is there initially in the fund? I am getting an equivalent interest rate: $J_2 = 0.0392$, and a present value for the total payments to be 991,741. Whats the correct thing to do?? 2. Originally Posted by Ife I am not sure what's the correct approach to this question. Can I get some guidance please?? As part of a retirement package for a local oil company, Jerry will receive$36,000 every 6 months for the next 20 years.
If the funds to fund this pension are invested at a rate of $J_1 = 8 \%$, how much money is there initially in the fund?

I am getting an equivalent interest rate: $J_2 = 0.0392$, and a present value for the total payments to be 991,741. Whats the correct thing to do??
.0392 is correct (3.92304845...%) IF 8% is effective annually;
if rate is 8% annual compounded semiannually, then use .04

991,741 is way too high; should be ~720,773
Try again.

3. Okay, I am not sure if I am totally correct but here's how i did it.

use the present value formula, PV=R[(1-(1+i)^-n)/i]

since Jerry receives $36,000 every 6 months then R(regular payment)=36,000, n(compounding periods)= 20x2=40(12/6=2) , and i(interest rate per compounding period)= 8%(.08/2)=0.04 sub. all the values into the formula and solve for PV and it will be the value of the initial fund. turn out to be approximately$712,539.86 which is the same as what Wilmer suggested.

Hope this helps. =]

4. That's correct, Fury, IF rate is 4% per 6months;
this then results in annual rate of 1.04^2 - 1 = .0816, or 8.16%.

IF annual rate is to be 8% (not 8.16) then 3.92% per 6months MUST be used.