kasiviv002
New member
- Joined
- May 24, 2011
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An annuity having a present value of A under a monthly compounded interest rate i pays out R dollars a month until the annuity is exhausted in n months. In each of he cases below, give a proof or counterexample.
(a) By doubling the value of A to 2A, the annuity will now last 2n months
(b) By doubling the interest rate i, the annuity can pay out 2R dollars for n months
I'm pretty sure I need to provide a counter example for both cases. This is what I did for a)
A= R ((1-(1+i)^(-n))/(i)
2A= (R ((1-(1+i)^(-n))/(i))(2)
2A= 2R ((1-(1+i)^(-n))/(i)
So the doubling effect of A, only effects R
For part b), I'm not quite sure how I would start..
(a) By doubling the value of A to 2A, the annuity will now last 2n months
(b) By doubling the interest rate i, the annuity can pay out 2R dollars for n months
I'm pretty sure I need to provide a counter example for both cases. This is what I did for a)
A= R ((1-(1+i)^(-n))/(i)
2A= (R ((1-(1+i)^(-n))/(i))(2)
2A= 2R ((1-(1+i)^(-n))/(i)
So the doubling effect of A, only effects R
For part b), I'm not quite sure how I would start..