Question

1) Sally needs $20,000 in 4 years. She has $10,000 to invest. If interest is compounded continuously, what rate is required for Sally to meet her goal?

Answer 1

`17.33\%`

Explanation:

we know that

The formula to calculate continuously compounded interest is equal to

`A=P(e)^(rt)`

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

`t=4\ years\\ A=\$20,000\\ P=\$10,000`

substitute in the formula above and solve for r

`20,000=10,000(e)^(4r)`

`2=(e)^(4r)`

Applying ln both sides

`ln(2)=4rln(e)`

`ln(2)=4r`

`r=ln(2)/4=0.1733`

Convert to percentage

`0.1733*100=17.33\%`