Question

Emma is going to invest in an account paying an interest rate of 3.7% compounded continuously. How much would Emma need to invest, to the nearest dollar, for the value of the account to reach $1,130 in 18 years?

Answer 1

$581

Step-by-step explanation:

The formula for continuous compound interest is

`P=Ae^(rt)`

where P is the final amount, A is the principal amount, r is the interest rate, and t is the time interval.

In Emma's case, r = 0.037 and P = 1130, and t = 18 years. Putting these values in the above formula and solving for A gives

`A=(P)/(e^(rt))`
`A=(1130)/(e^((0.037\cdot18)))`
`A=\$581.`

Hence, Emma needs to invest $581 today so that she has $1130 in her account after 18 years.