Compound interest is a type of exponential growth. Now imagine that
Lisa and Elicia each opened a new compound interest account.
Lisa deposited $20,000 into her compound interest account.
Elicia deposited $15,000 into her compound interest account.
Both accounts pay 5% interest annually.
No further deposits are made to the accounts and no withdrawals are made.
After 20 years, how much more interest would Lisa’s account earn than Elicia’s account? Round your answer to the nearest dollar.
~So dont i just change the percentage to a decimal, to 0.05. Then I would do 20000(0.05)^20 and 15000(0.05)^20? I dont know what to do after that.
20000*1.05^20 - 15000*1.05^20
= (20000-15000)*1.05^20
= 5000 * 1.05^20
or, consider that the difference is just the amount f interest earned by the extra $5000 that Lisa deposited.
5000*1.05^20
Note that the growth factor is 1.05, not just .05, since .05 gets smaller and smaller when raised to powers.
You're on the right track! To calculate the amount of interest earned by each account after 20 years, you need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, both accounts pay 5% interest annually, so the interest rate (r) is 0.05. Since the problem doesn't specify the compounding frequency, we'll assume it's compounded annually, so n = 1. And t = 20 years.
For Lisa's account:
P = $20,000
r = 0.05
n = 1
t = 20
Using the formula, you can calculate the final amount in Lisa's account after 20 years:
A1 = 20000(1 + 0.05/1)^(1*20)
Simplifying the equation, we have:
A1 = 20000(1.05)^20
For Elicia's account:
P = $15,000
r = 0.05
n = 1
t = 20
Similarly, you can calculate the final amount in Elicia's account after 20 years:
A2 = 15000(1 + 0.05/1)^(1*20)
Simplifying the equation, we have:
A2 = 15000(1.05)^20
Now, you just need to do the math and subtract the final amount in Elicia's account (A2) from the final amount in Lisa's account (A1):
Interest Earned = A1 - A2
After calculating this, you'll arrive at the amount of interest that Lisa's account would earn more than Elicia's account after 20 years. Remember to round your answer to the nearest dollar.