regular deposit compound interest Watch

rascal
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#1
Report Thread starter 12 years ago
#1
you have just won £4m in lottery. You have a choice of two options.
a) the whole amount right now
b) 500,000 a year for 10 years, the first payment starting exactly one year from now

assuming interest rates are 5% and compounded annually which option results in more money?

so we have to work out how much option b is worth right now but im not sure how to do that
anyone got any ideas?
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Itchynscratchy
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#2
Report 12 years ago
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£500,000 over 10 years is £5m.

So i assume the question is asking, is it better to have £4m now and have more interest or is it better to take the installments and be paid more overall.

well,

a) total = 4,000,000 x (1.05)^10 = £6.52m

b) total = 500,000 x 1.05 + 500,000 x (1.05)^2 + ..... 500,000 x (1.05)^10

= 500,000 x (1.05 + (1.05)^2 + (1.05)^3 ..... + (1.05)^10)

= £6.91m

So therefore option b is more profitable
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steve2005
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#3
Report 12 years ago
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(Original post by Itchynscratchy)
£500,000 over 10 years is £5m.

So i assume the question is asking, is it better to have £4m now and have more interest or is it better to take the installments and be paid more overall.

well,

a) total = 4,000,000 x (1.05)^10 = £6.52m

b) total = 500,000 x 1.05 + 500,000 x (1.05)^2 + ..... 500,000 x (1.05)^10

= 500,000 x (1.05 + (1.05)^2 + (1.05)^3 ..... + (1.05)^10)

= £6.91m

So therefore option b is more profitable
I disagree.

The final payment under option B is ten years from now. So there will be 10 years of interest on the £4000 000. There will be 9 years interest on the first £500 000 , 8 years on the second payment of £500 000.

I get total for Option A £6 515 579 and for Option B £6 288 946
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