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1. Quick problem on annuities

Hi i have another quick problem on the ASM problem on annuities

deposits of 1000 are placed into a fund at the beginning of each year for 30 years. At the end of the 40th year, annual payments commence and continue forever.

So if i draw the time line. 1000 is deposit on t=0 to t=29 which yields 30 years. then wouldnt i find the future value of that value from t=30 to t=40? which makes n=11? but the answer shows that they find the future value for n=9.

Thank you very much!

2. Originally Posted by iamsammy84
Hi i have another quick problem on the ASM problem on annuities

deposits of 1000 are placed into a fund at the beginning of each year for 30 years. At the end of the 40th year, annual payments commence and continue forever.

So if i draw the time line. 1000 is deposit on t=0 to t=29 which yields 30 years. then wouldnt i find the future value of that value from t=30 to t=40? which makes n=11? but the answer shows that they find the future value for n=9.

Thank you very much!
Actually, the deposits only span 29 years since the last deposit was made at t=29. Then we need an extra year to accumulate the interest on the last deposit which takes us to t=30. The first payment of the perpetuity-immediate will begin 1 year after last payment of previous annuity, which means we want the first annuity to end on the 39th year (at the end of the 39th year [t=39]), so the next annuity (perpetuity-immediate) can commence its first payment one year later at t=40.

So we have (for payments of R in the perpetuity with annual effective int. rate of i),

1000 s_30(..)@i * (1+i)^9 = R / i

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