Peter has $2000 invested in an account that gives him 5% interest a year. Write an equation for the amount of money, m, in his account after y, years. How much money will be in his account in 10 years, if he does not put any more in or take any out?

for compound interest

m = 2000 (1 + .05)^y

plug in 10 for y

What is the compounding frequency? Is it daily, monthly, or annually? We can't do compounded int. without knowing the frequency.

To write an equation for the amount of money in Peter's account after y years, we need to consider that the interest is compounded annually.

The formula for compound interest is given by:

A = P(1+r/n)^(n*t)

where:
A is the final amount,
P is the principal amount ($2000 in this case),
r is the annual interest rate (5% as a decimal, so 0.05),
n is the number of times interest is compounded per year (since it is compounded annually, n = 1),
and t is the number of years (y in this case).

So, for Peter's account after y years, the equation is:

m = 2000(1+0.05/1)^(1*y)

Simplifying this equation:

m = 2000(1+0.05)^y

Now, to find out how much money will be in Peter's account after 10 years, we substitute y = 10 into the equation:

m = 2000(1+0.05)^10

Calculating this:

m ≈ 2000(1.05)^10
m ≈ 2000(1.6289)
m ≈ $3257.80

Therefore, there will be approximately $3257.80 in Peter's account after 10 years if he does not put any more in or take any out.