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

The rate of interest monthly is 0.55%.

Given that,

The deposit amount is $4,600.The future value is $5,994.78The number of months = 4(12) = 48.The payment i.e. PMT = $0

Based on the above information, the calculation is as follows:

The formula is

= RATE(NPER,PMT,-PV,FV,TYPE)

After applying the above formula, the rate of interest monthly is 0.55%.

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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%.