MATH SOLVE

3 months ago

Q:
# 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?

Accepted Solution

A:

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%

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%