Its wrong. right answer is 12/20/28/37/42
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The invested amount, A=£4000
Rate of interest on this amount, r=5% per annum.
Total interest on the amount £4000 after 1 year
.
The total amount after 1 year, P=£4000+£200=£4200
Amount remains after an annual prize of £150=£4200-£150=£4050.
Note that after providing the annual prize the amount remains is £4050 which is more than the invested amount of £4000 as the prize money is less than the interest gained.
Now, for the 2nd year, the 5% interest is on the principal amount of £4050, which will have more interest as compared to the interest of 1st year.
Again, after prize distribution, the total amount remains for the principal amount of 3rd year will be more than the principal amount of 2nd year. This sequence repeated every year and the total amount will increase every year.
So, it will never end, the full prize money can be awarded for infinitely many years.