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# Geometric Series: Interest watch

1. I need some help with an interest study question in my course. The calculation of interest and such was introduced through geometric series, which I understand. The question reads: The cost of a life insurance policy is £55.89 in the first year. Subsequently
the cost in each year is 3% more than the cost in the previous year.
(a) Find the cost of the policy in the twentieth year.
(b) Find the total of all the payments made by the end of the twentieth
year.

I'm easily able to do a) but when I used my knowledge for part b I got an answer that doesn't seems right. With the info given, a=55.89 and r= 1.03 so the sum of 20 years should be
s20= (55.89(1.03^20 -1))/ (1.03-1)
which gives me 1501.79. Which doesn't seem right as wouldn't you reach this sum after only 3 years if you're paying 55.89 +3% each year? Is there another formula you need to use or some other information you need to put in, I could only use the knowledge I was given in the lesson ?
Thanks a bunch !
2. I'm confused - why do you think 3 years at roughly £55.89 would be more than £1501? The 3rd year payment is going to be 55.89 * (1.03)^2 = £59.29 < £60, so 3 years would be < £180.

Edit: Without detailed calculation, your sum of 1501 looks to be in the right ball park.
3. You don't reach that sum, or even close after paying for three years. You pay about 172 pounds. The answer you got is correct. I also calculated it for each year and summed it up to make sure, and I got the same answer. Besides, interest summing is a geometric series.

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Updated: January 30, 2017
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