Ben and Darcy each invest $4,000. Darcy’s investment earns 3% interest compounded annually. How much interest does she earn in 5 years?
(Round to the nearest hundredth
First, we need to find the amount of money Darcy will have after 5 years with a 3% interest rate compounded annually.
We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accumulated after n years, including interest
P = the principal amount (initial investment)
r = annual interest rate (decimal)
n = number of times the interest is compounded per year
t = number of years
In this case:
P = $4,000
r = 0.03
n = 1 (compounded annually)
t = 5
A = $4,000(1 + 0.03/1)^(1*5)
A = $4,000(1.03)^5
A = $4,000 * 1.159274
A = $4,637.09
Now, we can calculate the amount of interest earned by subtracting the initial investment from the total amount:
Interest = $4,637.09 - $4,000
Interest = $637.09
Therefore, Darcy earns $637.09 in interest after 5 years compounded annually at 3%.