1. ## Rate change

Code:
0 rate=9%=u%            1000.00=a

k rate=12%=v%

11=n                    3000.00=b
Ok, here's the dope:
1000 bucks deposited in savings account at year 0, at 9% compounded annually.
12% compounded annually will later be the rate, effective at a time k which will
result in a future value of 3000 bucks after 11 years.
For this to happen, k = 5.451118.....

If opening rate = u and opening deposit = a,
second rate = v , future value = b and number of years = n,
(v > u, b > a(1+u)^n)
what is k in terms of a,b,n,u,v?

2. Originally Posted by Wilmer
Code:
0 rate=9%=u%            1000.00=a

k rate=12%=v%

11=n                    3000.00=b
Ok, here's the dope:
1000 bucks deposited in savings account at year 0, at 9% compounded annually.
12% compounded annually will later be the rate, effective at a time k which will
result in a future value of 3000 bucks after 11 years.
For this to happen, k = 5.451118.....

If opening rate = u and opening deposit = a,
second rate = v , future value = b and number of years = n,
(v > u, b > a(1+u)^n)
what is k in terms of a,b,n,u,v?
After $\displaystyle $$k years at rate \displaystyle$$ r_1$, and $\displaystyle (N-k)$ years at rate $\displaystyle $$r_2 you have: \displaystyle b=a (1+r_1)^k(1+r_2)^{N-k} To solve for \displaystyle$$ k$ given $\displaystyle $$r_1, \displaystyle$$ r_2$, $\displaystyle $$N and \displaystyle$$ a$ is an excercise in the laws of logarithms.

CB

3. Yep...general case formula:

k = LOG[(1 + u) / (1 + v)] / LOG[b / a / (1 + v)^n]