# There are two people, one of them has $2000 and the other makes $300 a month. Create a savings plan that assures each has $10000 in 2 years.

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### 1 Answer

One of the persons has $2000 with her presently and the other makes $300 per month. A savings plan has to be created so that each of them has $10000 after 2 years.

The first person with $2000 can deposit the money in a bank. If the annual rate of interest is r, after two years the amount is equal to A=`2000*(1+r)^2`

=> `10000/2000 = (1+r)^2`

=> `5 = (1+r)^2`

=> `r = sqrt 5 - 1`

=> r = 23.60%

The rate of interest that should be given by the bank is equal to 23.6%. This is not a realistic rate of interest; it is not possible for her to have $10000 after 2 years with just $2000 to start with.

The second person makes $300 per month. If this amount is deposited in an account as a monthly payment for 24 months and the rate of interest received is r% every month, the amount after 2 years would be:

`A = 300+300*(1+r)+300*(1+r)^2+...300*(1+r)^24`

=> 10000 = `(300*(1+r)^25 - 1)/r`

The annual rate of interest required is 27.8%. This is also not a very realistic figure but in 2 years if only $300 are made every month it is not possible to accumulate $10000 at a lower rate of interest.