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

Answer:

$581

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=\frac{P}{e^{rt}}$$A=\frac{1130}{e^{(0.037\cdot18)}}$$A=\ 581.$

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