Question

How much money would you need to invest today at 3.5% annual interest compounded

continuously in order to accumulate $80,000 in 18 years?
The units are dollars, but do not enter the $ sign. Round two decimal places.

Answer 1

Answer: $ 42,607.34

Explanation:

Formula to find the accumulated amount ( compounded continuously ):

`A= Pe^(rt)`

,where P= principal amount

r= rate of interest

t= time

As per given , we have

A = $80,000

r= 3.5% = 0.035

t= 18 years

To find : P

Put all values in formula , we get

`80000=Pe^(0.035*18)\\\\\Rightarrow\ 80000=Pe^(0.63)\\\\\Rightarrow\ 80000=P(1.87761058)\\\\\Rightarrow\ P=(80000)/(1.87761057)\\\\\Rightarrow\ P=(80000)/(1.87761057)\\\\\Rightarrow\ P=42607.34`

Hence, $ 42,607.34 need to invest .