Actuarial Outpost Trouble with annuity time lines
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#1
01-30-2017, 12:23 AM
 mistersunnyd Member SOA Join Date: Aug 2016 Studying for how to find a job Posts: 175
Trouble with annuity time lines

A 30-year annuity is arranged to pay off a loan taken out today at a 5% annual effective interest rate. The first payment of the annuity is due in ten years in the amount of 1,000. The subsequent payments increase by 500 each year.
Calculate the amount of the loan.

I tried doing this problem like this: (v^10)*(1000 a double dot angle 30 at 5% + 500 Ia angle 29 at 5%), but something's wrong. Could anyone please explain? Thank you.
#2
01-30-2017, 12:30 AM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,472

#3
01-30-2017, 12:40 AM
 mistersunnyd Member SOA Join Date: Aug 2016 Studying for how to find a job Posts: 175

Ah my bad. I messed up the formula for increasing annuities...
#4
01-30-2017, 01:04 AM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,472

Try this

1000 + 500/.05 PMT
- 30 x 500/.05 FV
30 N
5 I/Y
CPT PV FV
0 PMT
9 N
CPT PV
#5
04-20-2018, 01:38 AM
 pxp91 SOA Join Date: Jan 2014 Posts: 1

Thanks for the reply. This might sound like a dumb question but I didn't quite get the keystrokes, could you please explain a bit?

Thanks a lot.