Compound Interest ALGEBRA 1

Question

You invest an initial $100 in an account that has an annual interest rate of 3%, compounded monthly. How much money will you have in the account after 20 years? Round your answer to the nearest cent

Answer 1

the underlying formula that you want to use here is

A = P(1 + r/n)^(nt)

for this scenario that means taking

A = 100(1 + 0.03/12)^(12*20)

A = 100(1.0025)^(240)

A = 182.08

meaning that you will have $182.08 in the account after 20 years

Answer 2

0.03/12 → interest earned every month

12 → number of times money is being compounded for 1 year

12y → number of times money is being compounded for “y” years

$100 → principle (money initially invested)

Money in the account after “y” years:

M = $100(1 + 0.03/12)^12y

M - money in the account

y - number of full years

Calculating the amount of money in the account in 20 years:

M = $100(1 + 0.03/12)^12•20 = $182.08

Answer 3

Why is it so difficult to plug in the given information??

A = P(1 + r/n)^nt

A = 100(1 + 0.03/12)¹²⁽²⁰⁾

Go.