Noah currently has an account balance of $2,976.45. He opened the account 11 years ago with a deposit of $1,963.45. If the interest compounds quarterly, what is the interest rate on the account?

What we know:

Acct. balance A (11) = $2,976.45

Pricipal=$1,963.45

Compounded (n) = quarterly (4)

rate=r

Compound interest formula: A (t) = p (1+r/n) ^nt

What we need toi find:

If the interest compounds quarterly, what is the interest rate on the account? Find r.

A (t) = p (1+r/n) ^nt

2976.45=1963.45 (1+r/4) ^ (4*11)

2976.45=1963.45 (1+r/4) ^44

2976.45/1963.45=1963.45/1963.45 (1+r/4) ^44

1.5159 = (1+r/4) ^44

(1.5159) ^ (1/44) = ((1+r/4) ^44) ^ (1/44)

1.0095=1+r/4

1.0095-1=1-1+r/4

.0095=r/4

.0095 (4) = r/4 (4)

.038=r

Rate = 3.8%