Question

Suppose an individual wants to have exactly 400,000 available for her child's education. a. Find the amount that would have to be invested at 13% compounded continuously, if the number of years until college is 6 years $ _______

Answer 1

For this individual, to accumulate $400,000 in a span of 6 years with continuous compounding at a rate of 13%, an approximate investment of 183362.4 dollars would be necessary.

How to get the amount

The formula we would use to solve this is given below:

`$400,000 = P * e^((0.13 * 6))`

in this formula

the principal is given as P while e is the exponential rate that the amount would have to increase.

Next we would try to expand the equation

`$400,000 = P * e^((0.78))`

From here we would have to get a formula for P. This would ve the subject of the equation

To do this, we are going to have to divide both sides by
`e^((0.78))`:

P = $400,000 /
`e^((0.78))`

P = 183362.4 dollars (rounded to the nearest cent)

Consequently, to accumulate $400,000 in a span of 6 years with continuous compounding at a rate of 13%, an approximate investment of 183362.4 dollars would be necessary.