Answer:
The nominal annual interest rate is 6%
Step-by-step explanation:
The future value of a sum of money an be calculated as follows,
FV = PV (1+i)^n
Where,
- PV is present value
- i is the interest rate
- n is the number of compounding periods
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%