# What is the simple interest rate for a fund that starts with \$1,550 on July 15,a deposit of \$730 37 days later, a withdrawal of \$250 100 days later, and abalance of \$2,211

tjbrewer | Certified Educator

Simple interest is applied by `V=P+Prt` We find the combined value of the fund by breaking the values into simpler sets of computations.

`V_1=1,550+1,550(37)(r)=1,550+57,350r` Is the value of the fund when the deposit was made.

`V_2=V_1+730` is the value of the fund after the deposit is made

After the fund completes its 100 day maturation, its value is the 2,211 in the account + the withdrawal of 250 for a final value of 2,461

`2,461=V_3=V_2+V_2(100-37)(r)=V_2+V_2(63)(r)`

We replace the values with their computed findings

`V_3=(V_1+730)+(V_1+730)(63)(r)=`

`((1,550+57,350r)+730)+((1,550+57,350r)+730)(63)(r)=`

`(2,280+57,350r)+(2,280+57,350r)(63)(r)=`

`(2,280+57,350r)+(143,640+3,613,050r)(r)=`

`(2,280+57,350r)+(143,640r+3,613,050r^2)=`

`2,280+200,990r+3,613,050r^2=2,461` We solve for 0

`3,613,050r^2+200,990r-181` and apply the Quadratic Formula

`r=(-200,990+-sqrt(40,396,980,100-4(3,613,050)(-181)))/(7,226,050)`

That comes out to r=.0886%/day or 32% APR