Find the nominal annual rate of interest compounded monthly if $1200 accumulates to $1618.62 in five years.

The nominal annual interest rate is 6%

Explanation:

The future value of a sum of money an be calculated as follows,

FV = PV (1+i)^n

Where,

As we already know the FV, the PV and the number of compounding periods, we can calculate the value of i. The value of i here represents the nominal annual interest rate denominated in monthly terms.

Annual interest rate denominated in monthly terms = Annual i / 12

As the total period in years is 5 years, the total period in monthly terms will be 5 * 12  = 60. So n is 60.

Plugging in the available values, we get the following expression which should be solved to get the monthly i.

1618.62  =  1200 * (1+i)^60

1618.62 / 1200 = (1+i)^60

1.34885 = (1+i)^60

Taking the 60th root of both sides.

(1.34885)^1/60  =  (1+i)^60/60

1.004999998  =  1 + i

1.00499998 - 1  = i

i = 0.00499998 rounded off to 0.005 or 0.5%

If the annual interest rate denominated in monthly terms is is 0.005 or 0.5%, then the annual interest rate is,

Annual interest rate = 0.005 * 12   = 0.06 or 6%

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