The Student Room Group

Annuity Investment (Compounding)

Question: Suppose you had a lump sum of £50,000 to invest in an annuity that will pay a monthly income for 10 years. If the issuing insurance company uses a nominal interest rate of 7% p.a compounded monthly, how much would your monthly income be?

My approach:

I found the effective yearly interest using the following formula:

((1+(i/n))^n)-1 => ((1+(0.07/12)^12)-1 => 0.07229 = ~7.23%

So I worked out the future value of £50,000 in 10 years time at an effective interest rate of 7.23% => £50,000(1.0723)^10 = £100,492.36

From this point, I divided by the number of time periods in question (Monthly payments*no. of years) => 12*10 = 120

£100,492.36/120 = £837.44 = Monthly Income

Is this the right way to go about this question, and is my solution correct?
(edited 9 years ago)
I think the answer you are looking for is similar to the last question you ask a bit earlier, but instead of finding the amount to invest, you are working out the monthly payments. If this is the case, then I would suggest you try to set it out the way I suggested in the last thread, this time, the £1000 is unknown, but the amount X is 50,000, you should understand how the calculation works from that.

http://www.thestudentroom.co.uk/showthread.php?t=2916667

I hope this helps.

PS: Your solution above doesn't seem to make sense, because the £100,492 you got there is the 10 year future value of the £50,000. Surely that cannot be the same as 120 lots of £837.44 which, although total to £100,492, is paid earlier than the £100,492. The 120 lots of payments's year 10 value is therefore different than its total, because as lots of these are paid before 10th year, it will attract interest during those periods.
(edited 9 years ago)
Original post by Anonynous
Is this the right way to go about this question, and is my solution correct?
No, and no. Listen to what chn.challenger has to say.

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