MATH SOLVE

2 months ago

Q:
# Find the interest rate for the given deposit and compound amount. $4600 accumulating to $5994.78, compounded monthly for 4 years.

Accepted Solution

A:

Here we use the classic formula for Compound Amount:

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

where P is the intial amount (i. e., the principal), r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

Then $5994.78 = $4600 (1 + r/12)^(4*12)

or ... $5994.78 = $4600 (1 + r/12)^48

We must solve for r.

Divide both sides of this equation by $4600:

1.303 = (1 + r/12)^48

Take the 48th root of both sides of this equation:

1.0056 = 1 + r/12

0.0056 = r/12 Solve for r: r = 12(0.0056) = 0.0672

The annual interest rate was 6.72%.

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

where P is the intial amount (i. e., the principal), r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

Then $5994.78 = $4600 (1 + r/12)^(4*12)

or ... $5994.78 = $4600 (1 + r/12)^48

We must solve for r.

Divide both sides of this equation by $4600:

1.303 = (1 + r/12)^48

Take the 48th root of both sides of this equation:

1.0056 = 1 + r/12

0.0056 = r/12 Solve for r: r = 12(0.0056) = 0.0672

The annual interest rate was 6.72%.