# sum

• June 16th 2008, 11:49 AM
VDestinV
sum
51. Jose wants to find a savings plan that will accumulate to $1 000 000 by the time he retires. He plans to retire in 35 years. He is willing to make monthly payments of$200. What interest rate will allow Jose to do this?

52. Investigate different savings plans that will accumulate to $100 000 after 15 years. • June 16th 2008, 12:47 PM TKHunny Quote: Originally Posted by VDestinV 51. Jose wants to find a savings plan that will accumulate to$1 000 000 by the time he retires. He plans to retire in 35 years. He is willing to make monthly payments of \$200. What interest rate will allow Jose to do this?

What have you tried? Your interest rate is not defined very well. This leaves the problem statement open to various interpretations. Shall we assume monthly compounding?

Let's say the MONTHLY effective rate is 'i' and r = 1+i

Then: $200*(r + r^{2} + r^{3} + ... + r^{35*12}) = 1000000$

Solve for 'i' and then maybe convert to ANNUAL EFFECTIVE or ANNUAL NOMINAL or whatever it is you think the question wants.

Hint: $r + r^{2} + r^{3} + ... + r^{35*12} = \frac{r-r^{421}}{1-r}$ if that helps.

Show you work. So far, I've seen nothing.